Question

Find x, y, z and t where, `[(z + t, x - y),(z - t, x + y)] = [(5, 3),(1, -1)]`

Answer 1

By the definition of equality of matrices, we have

z + t = 5   ...(i)

z − t = 1   ...(ii)

x − y = 3   ...(iii)

x + y = −1   ...(iv)

To find z and t, add (i) and (ii):

(z + t ) + (z − t) = 5 + 1

2z = 6

z = 3

Substitute z = 3 in (i):

3 + t = 5

t = 2

To find x and y, add (iii) and (iv)

(x − y) + (x + y) = 3 + (−1)

2x = 2

x = 1

Substitute x = 1 in (iii)

1 − y = 3

y = −2

Hence, x = 1, y = −2, z = 3, t = 2.