Question

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: (A – B)^T = A^T – B^T 

Answer 1

We have,

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

B = `[(4, 0),(1, 5)]`

C = `[(2, 0),(1, -2)]`

And a = 4, b = –2

(A – B)^T = `[(1 - 4, 2 - 0),(-1 - 1, 3 - 5)]^"T"`

= `[(-3, 2),(-2, -2)]^"T"`

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

Now A^T – B^T = `[(1, -1),(2, 3)] - [(4, 1),(0, 5)]`

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

= (A – B)^T 

Hence proved.