NCERT Solutions for Class 12 Mathemetics Chapter 3 - Matrices

Question 1:

In the matrix

(i) The order of the matrix.
(ii) The number of elements.
(iii) Write the elements a₁₃, a₂₁, a₃₃, a₂₄, a₂₃.

Question 2:

If a matrix has 24 elements, what are the possible orders it can have ? What, if it has 13 elements ?

Question 3:

If a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements ?

Question 4:

Construct a 2 x 2 matrix, A = [a_ij], whose elements are given by :

Question 5:

Construct a 3 x 4 matrix whose elements are given by :

Question 6:

Find the values of x, y and z from the following equations :

Question 7:

Find the values of a, b, c and d from the equation :

Question 8:

A = [a_ij]_{m x n} is a square matrix, if :

1. m < n
2. m > n
3. m = n
4. None of these

Question 9:

Which of the given values of x and y make the following pair of matrices equal ?

1. 

2. Not possible to find

3. 

4. 

Question 10:

The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is :

1. 27
2. 18
3. 81
4. 512

Question 11:

A + B

Question 12:

A - B

Question 13:

3A - C

Question 14:

AB

Question 15:

BA.

Question 16:

Compute the following :

Question 17:

Compute the following :

Question 18:

Compute the following :

Question 19:

Compute the following :

Question 20:

Compute the indicated products :

Question 21:

Compute the indicated products :

Question 22:

Compute the indicated products :

Question 23:

Compute the indicated products :

Question 24:

Compute the indicated products :

Question 25:

Compute the indicated products :

Question 26:

Question 27:

Question 28:

Question 29:

Find X and Y, if :

Question 30:

Find X and Y, if :

Question 31:

Question 32:

Question 33:

Solve the equation for x, y, z and t, if :

Question 34:

Question 35:

Question 36:

Show that f (x) f (y) = f (x + y).

Question 37:

Show that :

Question 38:

Show that :

Question 39:

Question 40:

Question 41:

Question 42:

Question 43:

A trust fund has ₹30,000 that must be invested in two different types of bonds. The first bond pays 5% and second 7% interest per year. Using matrix multiplication, determine how to divide ₹30,000 among the two types of bonds if the trust fund must obtain an annual total interest of :
(a) ₹1800 (b) ₹2000.

Question 44:

The book shop of a particular school has 10 dozen Chemistry books, 8 dozen Physics books, 10 dozen Economics books. The selling prices are ₹80, ₹60 and ₹40 each respectively. Find the total amount, the book-shop will receive from selling all the books, using matrix algebra.

Question 45:

The restriction on n, k and p so that PY + WY will be defined as :

1. k = 3, p = n
2. k is arbitrary, p = 2
3. p is arbitrary, k = 3
4. k = 2, p = 3.

Question 46:

If n = p, then the order of 7X - 5Z is :

1. p x 2
2. 2 x n
3. n x 3
4. p x n.

Question 47:

Find the transpose of each of the following matrices :

Question 48:

Find the transpose of each of the following matrices :

Question 49:

Find the transpose of each of the following matrices :

Question 50:

Question 51:

Question 52:

Question 53:

For the matrices A and B, verify that :
(AB)′ = B′A′, where :

Question 54:

For the matrices A and B, verify that :
(AB)′ = B′A′, where :

Question 55:

Question 56:

Question 57:

Show that the matrix

Question 58:

Show that the matrix

Question 59:

(i) A + A′ is a symmetric matrix
(ii) A - A′ is a skew-symmetric matrix.

Question 60:

Question 61:

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

Question 62:

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

Question 63:

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

Question 64:

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

Question 65:

Choose the correct answer
If A, B are symmetric matrices of same order, then AB - BA is a :

1. Skew-symmetric matrix
2. Symmetric matrix
3. Zero matrix
4. Identity matrix

Question 66:

Choose the correct answer

1. 

2. 

3. π

4. 

Question 67:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 68:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 69:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 70:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 71:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 72:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 73:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 74:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 75:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 76:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 77:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 78:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 79:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 80:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 81:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 82:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 83:

Using elementary transformations, find the inverse of each of the matrices, if it exists in

Question 84:

Matrix A and B will be inverse of each other if

1. AB = BA
2. AB = BA = O
3. AB = O, BA = I
4. AB = BA = I.

Question 85:

If A = [a_ij]_{m x n} is a square matrix, if :

1. m < n
2. m > n
3. m = n
4. None of these.

Question 86:

Which of the given values of x and y make the following pair of matrices equal :

1. 

2. Not possible to find

3. 

4. 

Question 87:

The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is :

1. 27
2. 18
3. 81
4. 512

Question 88:

Assume X, Y, Z, W and P are matrices of order 2 x n, 3 x k, 2 x p, n x 3 and p x k respectively. Now answer the following
The restrictions on n, k and p so that PY + WY will be defined are :

1. k = 3, p = n
2. k is arbitrary, p = 2
3. p is arbitrary
4. k = 2, p = 3

Question 89:

Assume X, Y, Z, W and P are matrices of order 2 x n, 3 x k, 2 x p, n x 3 and p x k respectively. Now answer the following
If n = p, then the order of the matrix 7X - 5Z is :

1. p x 2
2. 2 x n
3. n x 3
4. p x n

Question 90:

If A, B are symmetric matrices of same order, then AB - BA is a :

1. Skew-symmetric matrix
2. Symmetric matrix
3. Zero matrix
4. Identity matrix.

Question 91:

1. 

2. 

3. $\mathrm{\pi }$

4. 

Question 92:

Matrices A and B will be inverse of each other only if :

1. AB = BA
2. AB - BA = O
3. AB = O, BA = I
4. AB = BA = I

Question 93:

1. 1 + $\mathrm{\alpha }$² + $\mathrm{\beta }$$\mathrm{\gamma }$ = 0
2. 1 - $\mathrm{\alpha }$² + $\mathrm{\beta }$$\mathrm{\gamma }$ = 0
3. 1 - $\mathrm{\alpha }$² - $\mathrm{\beta }$$\mathrm{\gamma }$ = 0
4. 1 + $\mathrm{\alpha }$² - $\mathrm{\beta }$$\mathrm{\gamma }$= 0

Question 94:

If a matrix is both symmetric and skew-symmetric matrix, then :

1. A is a diagonal matrix
2. A is a zero matrix
3. A is a square matrix
4. None of these.

Question 95:

If A is a square matrix such that A² = A, then (I + A)³ - 7A is equal to :

1. A
2. I - A
3. I
4. 3A.