2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2

Students can Download Basic Maths Exercise 1.2 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2

Part – A

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

Question 1.
If A = \(\left[ \begin{matrix} 3 & 1 \\ 2 & 4 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} -1 \\ 3 \end{matrix} \right]\) . Find AB
Answers:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 1

Question 2.
If A = \(\left[ \begin{matrix} 1 & 2 \\ 0 & -3 \end{matrix} \right]\) . Find A2
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 2

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Question 3.
If A = \(\left[ \begin{matrix} 3 & -1 \\ 2 & -4 \end{matrix} \right]\) . Find A2
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 3

Question 4.
If A = \(\left[ \begin{matrix} 3 & 1 & 2 \\ 0 & -1 & 2 \\ -4 & 1 & -3 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right]\) . Find AB
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 4

Question 5.
If \(\left[ \begin{matrix} x \\ y \end{matrix} \right] =\left[ \begin{matrix} 2 & 3 \\ 1 & 0 \end{matrix} \right] \left[ \begin{matrix} 1 \\ 0 \end{matrix} \right]\) . Find x and y.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 5

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Question 6.
If \(\left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 1 & 0 & -1 \\ 2 & 0 & -1 \\ 0 & 1 & -2 \end{matrix} \right] \left[ \begin{matrix} 1 \\ 1 \\ 1 \end{matrix} \right]\) . Find x,y,z.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 6

Question 7.
If \(\left[ \begin{matrix} 4 \\ 1 \\ 3 \end{matrix} \right] \left[ \begin{matrix} x & y & z \end{matrix} \right] =\left[ \begin{matrix} 4 & 8 & 4 \\ 1 & 2 & 1 \\ 3 & 6 & 2 \end{matrix} \right]\) . Find x,y,z.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 7

Question 8.
If A = \(\left[ \begin{matrix} 1 \\ 4 \\ 2 \end{matrix} \right]\) anf B = \(\left[ \begin{matrix} 1 & 3 & 4 \end{matrix} \right]\) . Find AB.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 8

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Question 9.
Find A.B, if A = \(\left[ \begin{matrix} 1 & 3 & 2 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 4 \\ 2 \\ 1 \end{matrix} \right]\) .
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 9

Question 10.
Find x, if \(\left[ \begin{matrix} 2 & \times & 2 \end{matrix} \right] \left[ \begin{matrix} 1 \\ 4 \\ 2 \end{matrix} \right] =\left[ 3 \right] \) .
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 10
[2 + 4x + 4] = [3]
⇒ 4x = 3 – 6 = -3 ; x = \(\frac { -3 }{ 4 }\)

Part – B

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

Question 1.
If A = \(\left[ \begin{matrix} 2 & -2 \\ 3 & -1 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 3 & -1 \\ -2 & 0 \end{matrix} \right]\) . Find AB and BA
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 11

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Question 2.
If A = \(\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 1 & 4 & 2 \end{matrix} \right]\) .Find AB and BA.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 12

Question 3.
If A = \(\left[ \begin{matrix} 2 & 3 & -1 \\ 1 & -1 & 0 \end{matrix} \right]\) Find AA’ and A’A
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 13

Question 4.
If A = \(\left[ \begin{matrix} 3 & -1 & 2 \\ 1 & 2 & 2 \\ 2 & 0 & 5 \end{matrix} \right]\) , Find A2
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 14

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Question 5.
If A = \(\left[ \begin{matrix} 2 & 3 \\ -1 & 4 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 1 & -1 \\ 2 & 4 \end{matrix} \right]\) Find AB’ and A’B
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 15

Question 6.
If A = \(\left[ \begin{matrix} 2 & -1 \\ 1 & 4 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} -3 & 2 \\ -1 & 4 \end{matrix} \right]\) . show that (AB)’ = mB’A’
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 16

Question 7.
If A = \(\left[ \begin{matrix} 1 & 2 \\ 1 & 4 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 4 & -3 \\ 2 & 1 \end{matrix} \right]\) and C = \(\left[ \begin{matrix} 1 & 0 \\ -2 & 4 \end{matrix} \right]\) .
verify that (i) A(BC) = (AB)A (ii) A(B+C) = AB + AC
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 17

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Question 8.
If A = \(\left[ \begin{matrix} 1 & 3 \\ 1 & 0 \end{matrix} \right]\) . prove that A2 – A – 31 = 0
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 18
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 19

Question 9.
If A = \(\left[ \begin{matrix} 2 & -1 \\ -1 & 2 \end{matrix} \right]\) . Show that A2 – 4A + 31 = 0
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 20

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Question 10.
If A = \(\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right]\) Show that A2 – 5A = 21.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 21

Question 11.
Solve for x, y:
(i) \(\left[ \begin{matrix} 2 & -1 \\ 3 & 1 \end{matrix} \right] \left[ \begin{matrix} x \\ y \end{matrix} \right] =\left[ \begin{matrix} 10 \\ 2 \end{matrix} \right]\)
(ii) \(\left[ \begin{matrix} 1 & 3 \\ -2 & 4 \end{matrix} \right] \left[ \begin{matrix} x \\ y \end{matrix} \right] =\left[ \begin{matrix} -1 \\ 0 \end{matrix} \right]\)
(iii) \(\left[ \begin{matrix} x & y \end{matrix} \right] \left[ \begin{matrix} 2 & -1 \\ 3 & 1 \end{matrix} \right] =\left[ \begin{matrix} -1 & 4 \end{matrix} \right]\) .
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 22
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 23

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Question 12.
If x = \(\left[ \begin{matrix} 2 & 1 & 3 \\ 0 & 1 & 4 \end{matrix} \right]\) , y = \(\left[ \begin{matrix} 1 \\ 0 \\ 3 \end{matrix} \right]\) and z = [2 1]. verify that x(yz) = (xy)z.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 24
From 1 & 2 we get (xy)z = x(yz).

Part – C

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

Question 1.
If A = \(\left[ \begin{matrix} 2 & 3 \\ 1 & 0 \end{matrix} \right]\) and B = \(\left[ \begin{matrix} 2 & 1 & 4 \\ 0 & 1 & 3 \end{matrix} \right]\) . and C = \(\left[ \begin{matrix} 1 & -3 & -1 \\ -2 & 4 & 5 \\ 1 & 3 & -2 \end{matrix} \right]\) . verify (AB)C = A(BC).
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 25

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Question 2.
If A = \(\left[ \begin{matrix} 1 & 2 & -3 \\ 1 & -4 & 1 \\ 0 & 5 & 3 \end{matrix} \right]\) , B = \(\left[ \begin{matrix} 4 & -2 & -3 \\ 2 & -4 & -1 \\ 0 & 1 & 3 \end{matrix} \right]\) , C = \(\left[ \begin{matrix} 4 & 1 & 2 \\ 0 & 3 & 1 \\ -1 & -3 & 4 \end{matrix} \right]\) . verify (A + B)C = AC + BC.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 26
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 27
From 1 & 2 we get (A + B)C = AC + BC

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Question 3.
If A = \(\left[ \begin{matrix} i & 0 \\ 0 & -1 \end{matrix} \right]\) B = \(\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \end{matrix} \right]\) and C = \(\left[ \begin{matrix} 0 & i \\ i & 0 \end{matrix} \right]\) where i2 = -1, show that
(i) A2 = B2 = C2 = -1
(ii) AB = -BA = -C
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 28
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 29

Question 4.
If A = \(\left[ \begin{matrix} -1 & 1 & 0 \\ 3 & -3 & 3 \\ 5 & -5 & 5 \end{matrix} \right]\) , B = \(\left[ \begin{matrix} 0 & 4 & 3 \\ 1 & -3 & -3 \\ -1 & 4 & 4 \end{matrix} \right]\) . Show that A2 . B2 = A2.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 30
Hence A2B2 = A2 is proved.

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Question 5.
If f(x) = x2 – 5x + 7, find f(A) where A = \(\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \end{matrix} \right]\) .
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 31

Question 6.
If A = \(\left[ \begin{matrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{matrix} \right]\) B = \(\left[ \begin{matrix} 2 & 2 & -4 \\ -4 & 2 & 4 \\ 2 & -1 & 5 \end{matrix} \right]\) Show that BA = 61
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 32
Hence BA = 61 is proved

Question 7.
If A = \(\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right]\) and A + 2B = A2, find B
Answer:
Given A + 2B = A2
2B = A2 – A
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 33

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Question 8.
If \(\left[ \begin{matrix} 1 & 2 \\ 4 & 7 \end{matrix} \right] \left[ \begin{matrix} a & b \\ c & d \end{matrix} \right] =\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right]\) . Find a, b, c, d.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 34
∴ a = -7, b = 2, c = 4, d = -1.

Question 9.
If A = \(\left[ \begin{matrix} a & b \\ c & d \end{matrix} \right]\) and I = \(\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right]\) . Show that A2 – (a + d)A – (bc – ad) I is a null matrix.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 35

KSEEB Solutions

Question 10.
If A = \(\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right]\) . Prove that A2 – 4A – 51 is a null matrix of order 3 × 3.
Answer:
2nd PUC Basic Maths Question Bank Chapter 1 Matrices and Determinants Ex 1.2 - 36
∴ A2 – 4A – 51 is a null matrix.