Class12 ISC Chapter Matrices Exercise 3.4

Class XII ISC Maths Chapter Matrices Exercise 3.4

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

sinx	-cosx
cosx	sinx

0	6-5x
x²	x+3

3	√3	2
4	2	0

sinα	cosα
-cosα	sinα

Class XII ISC Maths Chapter Matrices Exercise 3.4

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Q1 If A= 2 -3 0 -1 4 5 , then find (3A)'.

Q2 If A= 2 -1 5 4 0 3 and B= -2 3 1 -1 2 -3 , then find A'+B'.

Q3 If A= sinx -cosx cosx sinx , 0< x< π/2 and A + A'=I where I is unity matrix, find the value of x

Q4 If AT= 3 4 -1 2 0 1 and B= -1 2 1 1 2 3 , then find AT - BT

Q5 If A= -1 5 3 7 , determine whether A + A' is symmetric or skew-symmetric.

Q6 If A= 5 -1 -2 6 , determine whether A - AT is symmetric or skew-symmetric.

Q7 If the matrix 0 6-5x x2 x+3 is symmetric, find the value(s) of x.

Q8 If A is a square matrix, prove that A'A is symmetric

Q9 If A, B are symmetric matrices and AB = BA, then show that AB is symmetric.

Q10 If A, B and AB are all symmetric matrices, then show that AB = BA

Q11 A, B are skew-symmetric matrices and AB = BA, then show that AB is symmetric

Q12 If A, B are skew-symmetric matrices of same order and AB is symmetric, then show that AB=BA

Q13 Let A= 5 -1 6 7 and B= 2 1 3 4 ,verify that (A')' = A (3A)'= 3A' (A-B)' = A'-B' (AB)' = B'A'

Q14 If A= 3 √3 2 4 2 0 and B= 2 -1 2 1 2 4 ,then verify that (A')' = A (A+B)' = A'+B' (k B)' = kB', where k is any real number

Q15 If A'= -2 3 1 2 and B= -1 0 1 2 , then find (A + 28)'

Q16 If A= 1 -4 3 and B= [-1 2 1] , verify that (AB)' = B'A'

Q17 If A= 1 2 4 1 5 6 and B= 1 2 6 4 7 3 ,then verify that

(i) (2A + B)' = 2A' + B'

(ii) (A - B)' = A' - B'

Q18 If A= 2 4 0 3 9 6 and B= 1 4 2 8 1 3 ,then verify that (AB)' = B'A'

Q19 If A= 3 2 -1 1 and B= -1 0 2 5 3 4 , find (BA)'.

Q20 If A= sinα cosα -cosα sinα ,then verify that A'A = I.

Q21 If A=1/3 1 -2 2 -2 1 2 -2 -2 -1 ,show that AA' = I.

Q22 Find the integral value of x if [x 4 -1] 2 -1 1 1 0 0 2 2 4 [x 4 -1]t=O

Q23 Show that the matrix A, where A= 1 -1 5 -1 2 1 5 1 3 , is a symmetric matrix.

Q24 Define a symmetric matrix. Prove that for A= 2 4 5 6 , A+ AT is a symmetric matrix where AT is the transpose of A.

Q25 If A= 2 3 4 5 ,prove that A - AT is a skew-symmetric matrix.

Q26 If A and B are symmetric matrices of the same order, prove that AB +BA is symmetric.

Q27 Express each of the following matrices as the sum of a symmetric and a skew-symmetric matrices :

(i) 3 5 1 -1

(ii) 3 -4 1 -1

Q28 Express the following matrices as the sum of symmetric and skew-symmetric matrices:

(i) 3 2 5 4 1 3 0 6 7

(ii) 2 4 -6 7 3 5 1 -2 4

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Q1 If
A=

2 -3 0

-1 4 5

, then find (3A)'.

Q2 If
A=

2 -1 5

4 0 3

and B=

-2 3 1

-1 2 -3

, then find A'+B'.

Q3 If
A=

sinx -cosx

cosx sinx

, 0< x< π/2 and A + A'=I where I is unity matrix, find the value of x

Q4 If
A^T=

3 4

-1 2

0 1

and B=

-1 2 1

1 2 3

, then find A^T - B^T

Q5 If
A=

-1 5

3 7

, determine whether A + A' is symmetric or skew-symmetric.

Q6 If
A=

5 -1

-2 6

, determine whether A - A^T is symmetric or skew-symmetric.

Q7 If the matrix

0 6-5x

x² x+3

is symmetric, find the value(s) of x.

Q13 Let
A=

5 -1

6 7

and B=

2 1

3 4

,verify that

(A')' = A

(3A)'= 3A'

(A-B)' = A'-B'

(AB)' = B'A'

Q14 If
A=

3 √3 2

4 2 0

and B=

2 -1 2

1 2 4

,then verify that

(A')' = A

(A+B)' = A'+B'

(k B)' = kB', where k is any real number

Q15 If
A'=

-2 3

1 2

and B=

-1 0

1 2

, then find (A + 28)'

Q16 If
A=

1

-4

3

and B= [-1 2 1]

, verify that (AB)' = B'A'

Q17 If
A=

1 2

4 1

5 6

and B=

1 2

6 4

7 3

,then verify that

Q18 If
A=

2 4 0

3 9 6

and B=

1 4

2 8

1 3

,then verify that (AB)' = B'A'

Q19 If
A=

3 2

-1 1

and B=

-1 0

2 5

3 4

, find (BA)'.

Q20 If
A=

sinα cosα

-cosα sinα

,then verify that A'A = I.

Q21 If
A=1/3

1 -2 2

-2 1 2

-2 -2 -1

,show that AA' = I.

Q22 Find the integral value of x if
[x 4 -1]

2 -1 1

1 0 0

2 2 4

[x 4 -1]^t=O

Q23 Show that the matrix A, where
A=

1 -1 5

-1 2 1

5 1 3

, is a symmetric matrix.

Q24 Define a symmetric matrix. Prove that for
A=

2 4

5 6

, A+ A^T is a symmetric matrix where A^T is the transpose of A.

Q25 If
A=

2 3

4 5

,prove that A - A^T is a skew-symmetric matrix.

(i)

3 5

1 -1

(ii)

3 -4

1 -1

(i)

3 2 5

4 1 3

0 6 7

(ii)

2 4 -6

7 3 5

1 -2 4