2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Students can Download Basic Maths Question Bank Chapter 1 Matrices and Determinants Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

Karnataka 2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

2nd PUC Basic Maths Matrices and Determinants One Mark Questions and Answers

Question 1.
If \(\mathbf{A}=\left[\begin{array}{c}3 \\-2 \\5\end{array}\right]\). Find AA’
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 1

Question 2.
If \({ A }=\left[ \begin{array}{l} 1 \\ 2 \\ 3 \end{array} \right] \).Find AA’
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 2

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 3.
If A = [1 0 2] \({ B }=\left[ \begin{array}{l} 1 \\ 2 \\ 3 \end{array} \right] \). Find AB.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 3

Question 4.
If A \(\mathbf{A}=\left[\begin{array}{ll}i & \mathbf{0} \\\mathbf{0} & i \end{array}\right]\) find A2
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 4

Question 5.
If [2 x 2] \(\left[\begin{array}{l}1 \\3 \\5\end{array}\right]\) = [9] S.T x = -1
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 5

Question 6.
Find x such that \(\left[\begin{array}{ll}3 & x \\4 & 7\end{array}\right]\) is symmentric
Answer:
x = 4

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 7.
Find x if [-1 x 4]\(\left[\begin{array}{c}1 \\2 \\-1\end{array}\right]\) = [3]
Answer:
– 1 +2x – 4 = 3
= 2x = 3 +5
x = 4

Question 8.
Give an example for scalar matrix
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 6

Question 9.
If \(\mathbf{A}=\left[\begin{array}{l}4 \\5 \\6\end{array}\right] \mathbf{B}=\left[\begin{array}{l}3 \\4 \\5\end{array}\right]\) compute 2A +3B
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 7

Question 10.
Find x if \(\left[\begin{array}{l}3 \\-1\end{array}\right]+\left[\begin{array}{l}2 x \\3
\end{array}\right]=\left[\begin{array}{l}1 \\2\end{array}\right]\)
Answer:
3x + 2x = 1 ⇒ 2x = -2  ⇒ x = -1

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 11.
A company sold 22 scooters, 15 cars and 10 buses in June and 20,21 and 11 respectively in October. Represent the data in the matrix form.
Answer:
\(M=\left[\begin{array}{lll} 22 & 15 & 10 \\20 & 21 & 11\end{array}\right]\)

Question 12.
The following matrix shows the belongings of 3 friends Amar, Akbar and Antony
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 8

Write down the row matrix which represents the belongings of Anthony.
Answer:
Anthonys belongings = [6 8].

Question 13.
Find x if \(\left|\begin{array}{cc}x & -3 \\-3 & x\end{array}\right|=0\)
Answer:
x2 – 9 = 0 ⇒ x = ± 3

Question 14.
Find x if  \(\left|\begin{array}{cc}2 x & -4 \\-2 & x\end{array}\right|=0\) then find x
Answer:
2x2 -8 = 0 ⇒ x2 = 4  ⇒ x = ± 2

Question 15.
Evalute \(\left|\begin{array}{cc}2 & 4 \\-5 & -1\end{array}\right|\)
Answer:
-2 + 20 = 18

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 16.
\(\left|\begin{array}{ll}\cos \theta & \sin \theta \\\sin \theta & \cos \theta\end{array}\right|\)
Answer:
Cosθ + sin2θ = 1

Question 17.
Evaluate \(\left|\begin{array}{ccc}1 & 5 & 7 \\5 & 25 & 35 \\3 & -1 & 0\end{array}\right|\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 9
= 5(0) = 0 (∴ Two rows are Indentical)

Question 18.
\(\mathbf{S} \mathbf{T}\left|\begin{array}{lll}\mathbf{1} & \mathbf{1 0} & \mathbf{2} \\\mathbf{2} & \mathbf{1 5} & \mathbf{2} \\\mathbf{3} & \mathbf{1 6} & \mathbf{6}\end{array}\right|=\mathbf{0}\) without expansion
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 10

Question 19.
If \(\left|\begin{array}{lll}2 & x & 3 \\4 & 1 & 6 \\1 & 2 & 7\end{array}\right|\) = 0 with out expansion.
Answer:
2(7-12)-x (28 – 6) +3(8 – 1) = 0
– 10 – 22x + 21 = 0 = x = 1/2

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 20.
Evaluate \(\left| \begin{matrix} 51 & 52 & 53 \\ 54 & 55 & 56 \\ 57 & 58 & 59 \end{matrix} \right| \) without expansion
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 11

Question 21.
Evaluate \(\begin{vmatrix} 3003 & 3005 \\ 3006 & 3008 \end{vmatrix}\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 12

Question 22.
If \( \mathbf{A}=\left[\begin{array}{lll}1 & 2 & 3 \\2 & x & 4 \\3 & 6 & 5
\end{array}\right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 13
⇒ (5x-24)-2(10-12) + 3(12 -3x) = 0
⇒ 5x – 24 + 4 + 36 – 9x = 0
⇒- 4x = – 16
x = 4

Question 23.
If \(\left(\begin{array}{ll}3 & 2 \\x & 6\end{array}\right)\) is singular, find x
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 14
= 2x – 18 = 0 ⇒ 2x = 18 ⇒ x = 9

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 24.
Without expanding
\({ S.T }\left| \begin{array}{lll} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{array} \right| =0\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 15

2nd PUC Basic Maths Matrices and Determinants Two Marks Questions and Answers

Question 1.
If \(\mathbf{A}=\left[\begin{array}{ll}3 & 2 \\4 & 1\end{array}\right]\) P.T. A2 – 4A – SI = 0. Where I is unit matrix and 0 is the null matrix of order 2 x 2
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 16

Question 2.
If \(\mathbf{A}+\mathbf{B}=\left[\begin{array}{ll}7 & \mathbf{0} \\2 & 5
\end{array}\right] \& \mathbf{A}-\mathbf{B}=\left[\begin{array}{ll}3 & 0 \\0 & 3\end{array}\right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 17

Question 3.
Find x and Y. If \(\left[\begin{array}{c}5 \\-3\end{array}\right]+\left[\begin{array}{ll}2 & x \\3 & y\end{array}\right]=\left[\begin{array}{l}1 \\6\end{array}\right]\)
Answer:
⇒ 5 + 2x = 1 and -3 +3y = 6
2x = 4 ⇒ x = 2
3y = 9 ⇒ y = 3

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 4.
If 2A + \( \mathbf{B}=\left[\begin{array}{cc}-7 & 11 \\7 & 4\end{array}\right] \& \mathbf{A}+\mathbf{2 B}=\left[\begin{array}{ll}-8 & 13 \\14 & 5\end{array}\right]\)find A. Multity equation 1 by 2 we get
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 18

Question 5.
Find AB if \(A=\left[\begin{array}{ll}3 & 2 \\5 & 1 \\1 & 1\end{array}\right] \quad B=\left[\begin{array}{l}1 \\3\end{array}\right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 19

Question 6.
Sukhesh buys 3 kgs of dal, 2 kgs of Rice and 5 kgs of oil if the cost of each is Rs. 25, Rs. 20 and Rs. 75 respectively, Find the total cost by matrix method.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 20

Question 7.
A lady buys 8 kgs of Apples, 4 kgs of Bananas and 6kgs of oranges. Apples cost Rs. 30 per kg, Bananas cost Rs. 15 per kgs and oranges cost Rs. 24 per kg. Obtain the total cost using matrices.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 21

Question 8.
If \(\mathbf{A}=\left[\begin{array}{lll}6 & 2 & 4 \\3 & 2 & 0\end{array}\right] \text { and } B=\left[\begin{array}{cc}1 & 2 \\1 & -1 \\2 & 4\end{array}\right]\) find
2A’ – 3B
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 22

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 9.
If \(\mathbf{A}=\left[\begin{array}{lll}2 & 1 & -3 \\1 & 2 & 1\end{array}\right] \mathbf{B}=\left[\begin{array}{cc}-3 & 2 \\1 & 4 \\1 & 5\end{array}\right]\)
find (AB)T
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 23

Question 10.
A company is considering which of the 3 methods of production it should be use in producing 3 products A, B and C. The amount of each product produced by each method is as shown below.
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 24
Answer:
Further information relating to profit per unit as follows
Product        A    B    C
Profit/unit    10   4   6
Using matrix multiplication find which method maximizes the total profit
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 25

Question 11.
If A = \(\mathbf{A}=\left[\begin{array}{cc}1 & -1 \\2 & 0 \\1 & -3\end{array}\right] \& \mathbf{B}=\left[\begin{array}{cc}-2 & 4 \\3 & 2 \\1 & 0\end{array}\right]\). Find 2A + 3B.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 26

Question 12.
If \(\left[\begin{array}{ll}x^{2} & 3 \\1 & 2\end{array}\right]+\left[\begin{array}{ll}5 x & 1 \\4 & 3\end{array}\right]=\left[\begin{array}{ll}6 & 4 \\5 & 5\end{array}\right]\). find x.
Answer:
x2 + 5x = 6
x2 + 5x – 6 – 0 (x + 6)(x – 1) = 0
x = – 6 or 1
[By adding and equating the correspondy terms].

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 13.
If \(\left[\begin{array}{ll}4 & 5 \\3 & 2\end{array}\right]+\left[\begin{array}{cc}2 & x-3 \\y-4 & 1\end{array}\right]=\left[\begin{array}{ll}6 & 1 \\2 & 3\end{array}\right]\) find x and y.
Answer:
5 + x – 3 = 1 ⇒ x = 1 – 2 = – 1
3 + y – 4 = 2 ⇒ y = 6 -3 = 3

Question 14.
If \(\mathbf{A}=\left[\begin{array}{ll}3 & -2 \\2 & 1\end{array}\right] \mathbf{B}=\left[\begin{array}{ll}1 & -1 \\6 & 2\end{array}\right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 27

2nd PUC Basic Maths Matrices and Determinants Three Marks Questions and Answers

Question 1.
If \(\mathbf{A}=\left[\begin{array}{cc}2 & -1 \\-3 & 1 \\4 & 0\end{array}\right] \quad \mathbf{B}=\left[\begin{array}{lll}3 & 1 & -5 \\5 & 4 & -2\end{array}\right]\) find AB and BA.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 28

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 2.
If \(A=\left[\begin{array}{ccc}2 & -1 & 3 \\-3 & 1 & 4 \\-2 & -1 & 5\end{array}\right]\) find A2
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 29

Question 3.
If \(\mathbf{A}=\left[\begin{array}{cc}2 & 3 \\-4 & 1\end{array}\right] \& \mathbf{B}=\left[\begin{array}{cc}-1 & 5 \\6 & 2\end{array}\right]\) S.T. (AB)’ = B’ A’
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 30

Question 4.
If \(\mathbf{A}=\left[\begin{array}{cc}2 & 3 \\1 & -1\end{array}\right] \& \mathbf{B}=\left[\begin{array}{l}-2 \\-1\end{array}\right]\) Find x such that Ax = B \(\text { Let } \mathbf{X}=\left[\begin{array}{l}x \\y\end{array}\right]=?\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 31

Question 5.
If \(A=\left[\begin{array}{ll}1 & 2 \\4 & 2\end{array}\right]\) then S T
|2A| = 4|A|
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 32
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 33

Question 6.
Find the inverse of the Matrix \(\text { (i) }\left[\begin{array}{ll}2 & 1 \\
3 & 2\end{array}\right] \text { (ii) }\left[\begin{array}{ll}2 & -1 \\3 & -2\end{array}\right]\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 34

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 7.
Solve the following equations by Cramer’s rule
(i) 5x + 7y – 3 = 0, 7x + 5y – 9=0
(ii) 4x – y = 5,3x + 2y =1
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 35
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 36

Question 8.
If \(\mathbf{A}=\left[\begin{array}{ll}1 & 2 \\3 & 4\end{array}\right] \quad B=\left[\begin{array}{cc}-1 & 0 \\0 & 1\end{array}\right]\) Find adj (AB)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 37

Question 9.
\(\mathbf{P T}\left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{b}+\boldsymbol{c} \\\boldsymbol{1} & \boldsymbol{b} & \boldsymbol{c}+\boldsymbol{a} \\\boldsymbol{1} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right|=\boldsymbol{0}\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 38
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 39

Question 10.
\(\text { S.T }\left|\begin{array}{lll} 2 & 2^{2} & 2^{3} \\2^{2} & 2^{3} & 2^{4} \\2^{4} & 2^{5} & 2^{6}\end{array}\right|=0\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 40

Question 11.
\(\mathbf{P T}\left|\begin{array}{lll}x-y & y-z & z-x \\a-b & b-c & c-a \\p-q & q-r & r-p\end{array}\right|=0 \)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 41

2nd PUC Basic Maths Matrices and Determinants Four Marks Questions and Answers

Question 1.
P.T \(\left|\begin{array}{lll}1 & 1 & 1 \\x & y & z \\x^{2} & y^{2} & z^{2}
\end{array}\right|\) = (x -y) (y – z) (z – x)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 42
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 43

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 2.
P.T \(\left|\begin{array}{lll}1 & x & y z \\1 & y & z x \\1 & z & x y\end{array}\right|\) = (x -y)(y – z)(z – x)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 44

Question 3.
S.T \(\left|\begin{array}{lll}x & y & y \\y & x & y \\y & y & x\end{array}\right|\)= (x+2y) (x – y)2
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 45
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 46

Question 2.
P. T \(\left|\begin{array}{lll}-a^{2} & a b & a c \\a b & -b^{2} & b c \\a c & b c & -c^{2}\end{array}\right|=4 a^{2} b^{2} c^{2}\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 47

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 4.
S. T \(\left|\begin{array}{ccc}1+a & b & c \\a & 1+b & c \\a & b & 1+c \end{array}\right|\) = 1 + a + b + c
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 48

Question 5.
P.T \(\left|\begin{array}{lll}x & p & q \\p & x & q \\p & q & x\end{array}\right|\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 49

Question 6.
P.T \(\left|\begin{array}{ccc}1 & y+z & y^{2}+z^{2} \\1 & z+x & z^{2}+x^{2} \\
1 \cdot x+y & x^{2}+y^{2}\end{array}\right|=(x-y)(y-z)(z-x)\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 50

Question 7.
If \(A=\left[\begin{array}{ll}1 & 3 \\4 & 5\end{array}\right]\) PT A adjA A =|A| I
Answer:

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 51

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 52

Question 8.
P. T\(\left|\begin{array}{ccc}a-b-c & 2 a & 2 a \\2 b & b-c-a & 2 b \\2 c & 2 c & c-a-b\end{array}\right|\) = (a + b + c )3 with out actnal expresian
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 53

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 9.
\({ ST }=\left| \begin{array}{ccc} { 1 }+{ a } & { 1 } & { 1 } \\ { 1 } & { 1+b } & { 1 } \\ { 1 } & { 1 } & { 1 }+{ c } \end{array} \right| ={ abc }({ 1+\frac { 1 }{ { a } } +\frac { { 1 } }{ { b } } +\frac { { 1 } }{ { c } } ) }\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 54
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 55

Question 10.
Solve for \(x:\left|\begin{array}{ccc}x+1 & x+2 & 3 \\3 & x+2 & x+1 \\x+1 & 2 & x+1\end{array}\right|=0\)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 56

Question 11.
Solve \(\left|\begin{array}{ccc}3 x-8 & 3 & 3 \\3 & 3 x-8 & 3 \\3 & 3 & 3 x-8 \end{array}\right|\) = 0 without direct expansion
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 57
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 58

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 12.
If \(\mathbf{A}=\left[\begin{array}{ccc}2 & 1 & -1 \\0 & 1 & 3 \\4 & 0 & 5
\end{array}\right]\)find A-1
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 59

Question 13.
Solve using cramers Rule
(i) 5x – y – 4z = 4, x +4y +2z = 12, 3x – y -z = 3
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 60
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 61

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 14.
Solve the following by Matrix Method:- 2x -y + z = 3, x +3y -2z =1, x+y+z = 6 The given equations is Matrix Method is
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 62

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 63

2nd PUC Basic Maths Matrices and Determinants Five or Six Marks Questions and Answers

Question 36.
A Salesman has the following record of sales during 3 months for 3 items A,B,& C which have different rates of commision.

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 64
Find out the reters of commission on iterm A,B & C11
Answer:
Let x, y & z denote the raters of commission in Rupees / unit for A,B&C iterms respec­tively. Then the data given can be expressed as a system of linear equations.
100x +100y + 200z = 900
300x+200y+ 100z= 1000
100x + 200y + 30z = 1400
x+y +2 z = 9
3x + 2y +z = 10
x + 2y + 3z
Solve these equations by Matrix Method.
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 65

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 66

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 37.
The Monthly expenditure an office for 3 months is given in the table
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 67
Assuming that the salary for the different Categories of the staft did net vary from months to month, calculate the salary for each type of staft per Month.
Answer:
Let the Salary of the clerks, peon & typists be x, y,& z
8x + 4y + 6z = 3750
9x +9y + 6z = 5000
12x + 9y + 12z = 8850
The given equation in Matrix form is
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 68

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 69

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 38.
TheThe prices of 3 commodities X,Y,Z are x,y,z & respectively. A sells 4 units of Z & purchases 24 units of X & 5 units of Y. B Sells 5units of Y, & purchases 1 unit of X and 1 unit of Z.C sells 1 unit of X, 1 unit of Z and purchases 1 units of Y. In the process Rs 700, Rs 350 & 250 remain with A, B & C respective. Find the pice / unit of X
Answer:
The given data in Matrix form is
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 70
A x = B ⇒ x = A-1B
where  x is the price of X
y is the price of Y z is the price of Z
Here purchase is indicated by α – ve Sign & Sales is indicated by α + ve sign.
By Solve the equation by Matrix Method we get x = 150, y = 200 & z = 500

Question 39.
The cost of 4 kg Ragi, 3kg rice & 2 kg wheat is ₹60, the cost of 2kg Ragi, 4kgs rice & 6kg wheat is ₹90. The cost of 6 kg Ragi, 2kg Rice & 3kg wheat is ₹70. Find the cost of each item per kg by Matrix Method.
Answer:
Let the prices (per kg) of Ragi, Rice & wheat be ₹x,& Xz, respectively then the data in the system of equations is given by
4x + 3y + 2z = 60
2x + 4y + 6z = 90
6x + 2y + 3z = 70
These equation in form of Matrix is
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 71
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 72

Question 40.
The Sum of three nembers 3 is 6. If we maltiply third number by 3 & add second num­ber to it, we get 11 By adding I and III numbers, we get doduble of the 2nd number Represent it algebraically and find the number 8 using matrix method.
Answer:
Let the I, II & III nos be donoted by x,y & z respectively. Then according to given conditions we have, x + y + z = 6
y + 32 = 11
x + z = 2y ⇒ x – 2y + z ≠ 0                                                    .
These equations can be put in Matrix form as
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 73
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 74

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 41.
Food I has one unit of Vitamin A, 2 units of vitamin &units of Vitamin C Food II has 1,3 & 9 units respectively & Food III has 1, 2 & 1 unit respectively units of vitamin A, 17 units of vitamin in & 37 units of vitamin C are required. Find all possible amount 3 foods that will provide exactly these amounts of the vitamins.
Answer:
Let x, y & z be the amounts of the food I, II & III respectively. Then we have the following ret of simaltaneous linear equations.
x + y + z = 7
2x + 3y + 2z = 17
4x + 9y + z = 37
By using Matrix Method Solve the above equations The given equations in Matrix form
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 75
|A|= 1(3 – 18)-1(2 – 8)+ 1(18 – 12)
= -15 + 6 + 6 =-3 ≠ 0 ∴ A-1 exists
By Solving the equation X = A-1B we get
x = 2, y = 3, z = 2

Question 42.
PT \(\left|\begin{array}{lll}1 & 1 & 1 \\a & b & c \\a^{3} & b^{3} & c^{3} \end{array}\right|\) = (a – b) (b – c) (c – a)(a + b +c)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 76
= (a- b)(b – c) [(c – a)(c + a) +b(c – a)]
= (a – b)(b – c)(c – a)(a+b+c) = R.H.S

Question 43.
ST\(\left|\begin{array}{ccc}1 & 1 & 1 \\x^{2} & y^{2} & z^{2} \\x^{3} & y^{3} & z^{3} \end{array}\right|\)=(x – y)(y – z)(xy + yz + zx)
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 77
x2y (x – y) (y – z)[(xz2 – x2z) + (yz2 – x2y) ]
(x – y)(y – z)[x = (z – x) + y(z2 – x2)]
(x – y)(y – z)(z – x)[zx + y(z + x)]
(x – y)(y – z)(z – x)(xy + yz + zx) = R.H.S

2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants

Question 44.
If \(A=\left[\begin{array}{lll}1 & 2 & 3 \\1 & 3 & 4 \\1 & 4 & 3\end{array}\right]\) verify A adj A . A = |A|
Answer:
|A| = 1(9 – 16) -2(3 – 4) + 3(4 -3)
= (-7) + 2 + 3 = -2
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 78
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 79

Question 45.
If A = \(=\left[\begin{array}{lll}1 & 2 & 3 \\1 & 3 & 4 \\1 & 4 & 3\end{array}\right]\) then verify A adj A =|A|. I
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants 80

shares