Question

`A = [(-6, 0),(4, 2)]` and `B = [(1, 0),(1, 3)]`. Find matrix M, if `M = 1/2 A - 2B + 5l`, where l is the identity matrix.

Answer 1

Given: `A = [(-6, 0), (4, 2)]` 

`B = [(1, 0), (1, 3)]` 

`M = 1/2 A - 2B + 5I` (I is 2 × 2 identity)

`1/2 A = 1/2 xx [(-6, 0), (4, 2)]` 

= `[(-3, 0), (2, 1)]` 

`-2B = −2 xx [(1, 0), (1, 3)]` 

= `[(-2, 0), (-2, -6)]` 

`5I = [(5, 0), (0, 5)]`

Add them elementwise:

`M = [(-3, 0), (2, 1)] + [(-2, 0), (-2, -6)] + [(5, 0), (0, 5)]` 

= `[(-3 - 2 + 5, 0 + 0 + 0), (2 - 2 + 0, 1 - 6 + 5)]` 

= `[(0, 0), (0, 0)]`

`M = [(0, 0), (0, 0)]` the 2 × 2 zero matrix.