# Equality of two Matrices

Two matrices A = [a_{ij}] and B = [b_{ij}] are said to be equal if they are of same order and each element of A is equal to the corresponding element of B, that is a_{ij} = b_{ij} for all i and j. Symbolically we write it as A = B

Find the values of a, b, c, x, y and z

Solution: Since the matrices are equal, corresponding elements are equal

x + 3 = 0

x = -3

z + 4 = 6

z = 2

2y – 7 = 3y - 2

2y - 3y = -2 + 7

y = -5

a – 1 = -3

a = -2

2c + 2 = 0

c = -1

b – 3 = 2b + 4

b - 2b = 7

b = -7

Hence, a = -2, b = -7, c = -1, x = -3, y = -5 and z = 2.

Try this:

1. Given that the following matrices are equal, find the values of x and y.

(Answer: x = 1, y = 4)

2. Given that the following matrices are equal, find the values of x, y, and z.

(Answer: x = 4, y = –6, and z = 9)

## Construction of a Matrix

When the general term and the order of a matrix is given, we can easily construct a matrix.

For example: Construct a 3 x 4 matrix whose elements are given by a_{ij} = 2i - j

a11 = 2 – 1 = 1 a_{12} = 2 – 2 = 0 a_{13} = 2 – 3 = -1 a_{14} = 2 – 4 = -2

a_{21} = 4 – 1 = 3 a_{22} = 4 – 2 = 2 a_{23} = 4 – 3 = 1 a_{24} = 4 – 4 = 0

a_{31} = 6 - 1 = 5 a_{32} = 6 – 2 = 4 a_{33} = 6 – 3 = 3 a_{34} = 6 – 4 = 2

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### Reference Links:

- http://en.wikipedia.org/wiki/Matrix_(mathematics)
- http://www.mathreference.com/la-mpoly,order.html
- http://wiki.answers.com/Q/What_is_order_of_the_resultant_matrix_AB_when_two_matrices_are_multiplied_and_the_order_of_the_Matrix_A_is_m_n_order_of_Matrix_B_is_n_p_Also_state_the_condition_under_which_two_matrices_can_be_mult