Here you will learn equality of matrices definition with examples.
Let’s begin –
Equality of Matrices
Definition : Two matrice A = [aij]m×n and B = [bij]r×s are equal if
(i) m = r i.e. the number of rows in A equals the number of rows in B.
(ii) n = s i.e the number of columns in A equals the number of columns in B.
(iii) aij = bij for i = 1, 2, ……. , m and j = 1, 2, ,,,,, , n.
If two matrices A and B are equal, we write A = B, otherwise we write A ≠ B.
The matrices A = [321xy51−14] and B = [321−105−1−1z] are equal if x = -1, y = 0 and z = 4.
Matrices [0000] and [000000] are not equal, because their orders are not same.
Example : Find the value of x, y, z and w which satisfy the matrix equation, [x–y2x+z2x–y3z+w] = [−15013]
Solution : Since the corresponding elements of two equal matrices are equal. Therefore,
[x–y2x+z2x–y3z+w] = [−15013]
⟹ x – y = -1, 2x + z = 5, 2x – y = 0, 3z + w = 13
Solving the equation x – y = -1 and 2x- y = 0 as simultaneous linear equations, we get x = 1 and y = 2.
Now, putting x = 1 in 2x + z = 5, we get z = 3. Substituting z = 3 in 3z + w = 13, we obtain w = 4
Thus, x = 1, y = 2, z = 3 and w = 4