Question

Given matrix B =`[(1,1), (8,3)]` Find the matrix X if, X = B² - 4B. Hence, solve for a and b given X`[(a), (b)] = [(5), (50)]`

Answer 1

`B^2 = B xx B = [(1,1), (8,3)][(1,1), (8,3)] = [(1xx1+1xx8,1xx1+1xx3), (8xx1+3xx8,8xx1+3xx3)] = [(9,4), (32,17)]`

4B = 4`[(1,1), (8,3)] = [(4,4), (32,12)]`

Given : `X = B^2 - 4B`

`=> X = [(9,4), (32,17)] - [(4,4), (32,12)] = [(5,0), (0,5)]`

To find: a and b

X`[(a), (b)] = [(5), (50)]` ........given

`=> [(5,0), (0,5)][(a), (b)] = [(5), (50)]`

`=> [(5a), (5b)] = [(5), (50)]`

`=> 5[(a), (b)] =  5[(1), (10)]`

`=> a = 1 and b = 10