Class12 ISC Chapter Matrices Exercise 3.2

Class XII ISC Maths Chapter Matrices Exercise 3.2

Explore our extensive collection of questions on the topic of "Matrices," designed to help you master this fundamental concept in mathematics. Our question bank covers a wide range of topics, including matrix operations, types of matrices, determinants, inverses, and applications of matrices in solving linear equations. These practice questions are perfect for students aiming to build a strong foundation in matrices and excel in their exams. Whether you're studying for class or looking to enhance your understanding, our curated collection offers the ideal resource for mastering "Matrices."

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Matrices

a² +b²	b² + c²
a² + c²	a² + b²

2ab	2bc
-2ac	-2ab

cos²x	sin²x
sin²x	cos²x

sin²x	cos²x
cos²x	sin²x

Class XII ISC Maths Chapter Matrices Exercise 3.2

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Q1 If A= 2 4 3 2 ,B= 1 3 -2 5 and C= -2 5 3 4 ,find the following : A+B A-B 3A-C

Q2 Compute the following:

(i) a b -b a + a b b a

(ii) a2 +b2 b2 + c2 a2 + c2 a2 + b2 + 2ab 2bc -2ac -2ab

(iii) -1 4 -6 8 5 16 2 8 5 + 12 7 6 8 0 5 3 2 4

(iv) cos2x sin2x sin2x cos2x + sin2x cos2x cos2x sin2x

Q3 If A= 1 5 -2 3 and B= 0 -1 4 -7 ,find 2A-3B

Q4 If B= -1 5 0 3 and A-2B= 0 4 -7 5 ,find the matrix A

Q5(i) If A= 1 2 3 2 3 1 and B= 3 -1 3 -1 0 2 ,then find 2A-B

Q5(ii) If 9 -1 4 -2 1 3 = A+ 1 2 -1 0 4 9 ,then find the matrix A

Q6 If A=diagonal [1, -2, 5], B = diagonal [3, 0, -4] and C = diagonal [-2, 7, 0], then find A+2B-3C

Q7 If A= 2 -3 5 0 and kA= 8 3a -2b c ,find the values of k, a, b and c.

Q8 If x 2 3 +y -1 1 = 10 5 ,find the values of x and y.

Q9 If 2 1 3 0 x + y 0 1 2 = 5 6 1 8 ,find the values of x and y.

Q10 Given 2 x z y t +3 1 -1 0 2 = 3 3 5 4 6 ,find x,y,z,t.

Q11 If 3 a b c d = a 6 -1 2d + 4 a+b c+d 3 ,find a, b, c and d.

Q12 Find X if Y= 3 2 1 4 and 2X + Y= 1 0 -3 2

Q13 Find matrices X and Y, if X + Y= 7 0 2 5 and X -Y = 3 0 0 3

Q14 Find matrices X and Y if 2X-Y= 6 -6 0 -4 2 1 and X +2Y = 3 2 5 -2 1 -7

Q15 If A= 1 3 2 1 3 -1 and B= 2 1 1 2 -1 0 ,find the matrix C such that A+ B+ C is a zero matrix

Q16 Find a matrix X such that 3A-2B+ X = O, where A= , B= 4 2 1 3 -2 1 3 2

Q17 If A= 9 1 7 8 and B= 1 5 7 12 ,find matrix C such that 5A +3B + 2C is a null matrix.

Q18 If A= 8 0 4 -2 3 6 and B= 2 -2 4 2 -5 1 ,then find matrix X such that 2A +3X =5B

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Q1 If
A=

2 4

3 2

,B=

1 3

-2 5

and C=

-2 5

3 4

,find the following :

A+B

A-B

3A-C

(i)

a b

-b a

+

a b

b a

(ii)

a² +b² b² + c²

a² + c² a² + b²

+

2ab 2bc

-2ac -2ab

(iii)

-1 4 -6

8 5 16

2 8 5

+

12 7 6

8 0 5

3 2 4

(iv)

cos²x sin²x

sin²x cos²x

+

sin²x cos²x

cos²x sin²x

Q3 If
A=

1 5

-2 3

and B=

0 -1

4 -7

,find 2A-3B

Q4 If
B=

-1 5

0 3

and A-2B=

0 4

-7 5

,find the matrix A

Q5(i) If
A=

1 2 3

2 3 1

and B=

3 -1 3

-1 0 2

,then find 2A-B

Q5(ii) If

9 -1 4

-2 1 3

= A+

1 2 -1

0 4 9

,then find the matrix A

Q7 If
A=

2 -3

5 0

and kA=

8 3a

-2b c

,find the values of k, a, b and c.

Q8 If
x

2

3

+y

-1

1

=

10

5

,find the values of x and y.

Q9 If
2

1 3

0 x

+

y 0

1 2

=

5 6

1 8

,find the values of x and y.

Q10 Given
2

x z

y t

+3

1 -1

0 2

= 3

3 5

4 6

,find x,y,z,t.

Q11 If
3

a b

c d

=

a 6

-1 2d

+

4 a+b

c+d 3

,find a, b, c and d.

Q12 Find X if Y=

3 2

1 4

and 2X + Y=

1 0

-3 2

Q13 Find matrices X and Y, if X + Y=

7 0

2 5

and X -Y =

3 0

0 3

Q14 Find matrices X and Y if
2X-Y=

6 -6 0

-4 2 1

and X +2Y =

3 2 5

-2 1 -7

Q15 If
A=

1 3

2 1

3 -1

and B=

2 1

1 2

-1 0

,find the matrix C such that A+ B+ C is a zero matrix

Q16 Find a matrix X such that 3A-2B+ X = O, where
A=
, B=

4 2

1 3

-2 1

3 2

Q17 If
A=

9 1

7 8

and B=

1 5

7 12

,find matrix C such that 5A +3B + 2C is a null matrix.

Q18 If
A=

8 0

4 -2

3 6

and B=

2 -2

4 2

-5 1

,then find matrix X such that 2A +3X =5B