Chapter 3 MATRICES EXERCISE 3.1

NCERT Solutions for Class 12 Maths – Chapter 3 – MATRICES EXERCISE 3.1

NCERT Solutions for Class 12 Maths – Chapter 3 – MATRICES EXERCISE 3.2

Question 1. In the matrix

    2  5  19  -7
    35 -2  5/2  12
    √3  1  -5  17
    

write:
(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?

Question4. Construct a 2 × 2 matrix, A = [aij], whose elements are given by:
(i) a_ij = (i + j)² / 2
(ii) a_ij = i / j
(iii) a_ij = (i + 2j) ² / 2

Question 5. Construct a 3 × 4 matrix, whose elements are given by:
(i) a_ij = 1/2 | -3i + j |
(ii) a_ij = 2i - j

Question 6. Find the values of x, y and z from the following equations:
(i)

    [ 4  3 ]      =   [ y  z ]
    [ x  5 ]          [ 1  5 ]      
    

(ii)

    [ x+y  2 ]      =   [ 6  2 ]
    [ 5+z  xy]          [ 5  8 ]
    

(ii)

    [ x+y  2 ]      =   [ 6  2 ]
    [ 5+z  xy]          [ 5  8 ]
    

(iii)

    [ x+y+z  ]       [ 9 ]
    [ x+z    ]   =   [ 5 ]
    [ y+z    ]       [ 7 ]
    
    

Question 7. Find the value of a, b, c and d from the equation:

    [ a-b     2a + c ]   =      [ -1  5 ]
    [ 2a - b  3c + d ]          [ 0  13 ]
    

Question 8. A = [a_ij] _{m × n} is a square matrix, if
(A) m < n
(B) m > n
(C) m = n
(D) None of these

Question 9. Which of the given values of x and y make the following pair of matrices equal
(A) x = -1/3 , y = 7
(B) Not possible to find
(C) y = 7 , x = -2/3
(D) x = -1/3 , y = -2 /3

Question 10. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:
(A) 27
(B) 18
(C) 81
(D) 512

12 Mathematics chapter 3 Solution of Question 1 to 10

1. Matrix: An ordered rectangular array of numbers or functions.
2. Matrix Order: A matrix having _m rows and _n columns is called a matrix of order _{m × n}.
3. Column Matrix: _{[aij] m × 1} is a column matrix.
4. Row Matrix: _{[aij] 1 × n} is a row matrix.
5. Square Matrix: An _{m × n} matrix is a square matrix if _{m = n}.
6. Diagonal Matrix: A = [a_ij] _{m × m} is a diagonal matrix if _{aij = 0}, when _{i ≠ j}.
7. Scalar Matrix: A = [a_ij] _{n × n} is a scalar matrix if _{aij = 0}, when _{i ≠ j}, _{aij = k} (where _k is some constant), when _{i = j}.
8. Identity Matrix: A = [a_ij] _{n × n} is an identity matrix if _{aij = 1}, when _{i = j}, _{aij = 0}, when _{i ≠ j}.
9. Zero Matrix: A zero matrix has all its elements as zero.
10. Equality of Matrices: A = [a_ij] = [b_ij] = B if (i) A and B are of the same order, (ii) _{aij = bij} for all possible values of _i and _j.