Question

Find the matrix M such that `[(5, -7),(-2, 3)] M = [(-16, -6),(7, 2)]`.

Answer 1

The given equation is of the form AM = B,

A = `[(5, -7),(-2, 3)] B = [(-16, -6),(7, 2)]`

To solve for M, multiply both sides by the inverse of A from the left:

M = A⁻¹ B

Find determinant (A):

(A) = (5)(3) − (−7)(−2)

= 15 − 14

= 1

Since the determinant is 1, the inverse A⁻¹ is:

A⁻¹ = `1/1[(3, 7),(2, 5)]`

= `[(3, 7),(2, 5)]`

Perform matrix multiplication

M = `[(3, 7),(2, 5)] xx [(-16, -6),(7, 2)]`

= `[(3 xx (-16) + 7 xx 7, 3 xx (-6) + 7 xx 2),(2 xx (-16) + 5 xx 7, 2 xx (-6) + 5 xx 2)]`

= `[(-48 + 49, -18 + 14),(-32 + 35, -12 + 10)]`

= `[(1, -4),(3, -2)]`