# 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

Question 2.
If A = $$\left[ \begin{matrix} 1 & 2 \\ 0 & -3 \end{matrix} \right]$$ . Find A2

Question 3.
If A = $$\left[ \begin{matrix} 3 & -1 \\ 2 & -4 \end{matrix} \right]$$ . Find A2

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

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.

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.

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.

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.

Question 9.
Find A.B, if A = $$\left[ \begin{matrix} 1 & 3 & 2 \end{matrix} \right]$$ and B = $$\left[ \begin{matrix} 4 \\ 2 \\ 1 \end{matrix} \right]$$ .

Question 10.
Find x, if $$\left[ \begin{matrix} 2 & \times & 2 \end{matrix} \right] \left[ \begin{matrix} 1 \\ 4 \\ 2 \end{matrix} \right] =\left[ 3 \right]$$ .

[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

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.

Question 3.
If A = $$\left[ \begin{matrix} 2 & 3 & -1 \\ 1 & -1 & 0 \end{matrix} \right]$$ Find AA’ and A’A

Question 4.
If A = $$\left[ \begin{matrix} 3 & -1 & 2 \\ 1 & 2 & 2 \\ 2 & 0 & 5 \end{matrix} \right]$$ , Find A2

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

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’

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

Question 8.
If A = $$\left[ \begin{matrix} 1 & 3 \\ 1 & 0 \end{matrix} \right]$$ . prove that A2 – A – 31 = 0

Question 9.
If A = $$\left[ \begin{matrix} 2 & -1 \\ -1 & 2 \end{matrix} \right]$$ . Show that A2 – 4A + 31 = 0

Question 10.
If A = $$\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right]$$ Show that A2 – 5A = 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) $$\left[ \begin{matrix} x & y \end{matrix} \right] \left[ \begin{matrix} 2 & -1 \\ 3 & 1 \end{matrix} \right] =\left[ \begin{matrix} -1 & 4 \end{matrix} \right]$$ .

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.

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).

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.

From 1 & 2 we get (A + B)C = AC + BC

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

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.

Hence A2B2 = A2 is proved.

Question 5.
If f(x) = x2 – 5x + 7, find f(A) where A = $$\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \end{matrix} \right]$$ .

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

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
Given A + 2B = A2
2B = A2 – A

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.

∴ 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.
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.