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

Given B = `[(1, 1),(8, 3)]` and X = B² – 4B

Now B² = B × B

= `[(1, 1),(8, 3)] xx [(1, 1),(8, 3)]`

= `[(1 xx 1 + 1 xx 8, 1 xx 1 + 1 xx 3),(8 xx 1 + 3 xx 8, 8 xx 1 + 3 xx 3)]`

= `[(1 + 8, 1 + 3),(8 + 24, 8 + 9)]`

= `[(9, 4),(32, 17)]`

X = B² – 4B

= `[(9, 4),(32, 17)] - 4[(1, 1),(8, 3)]`

= `[(9, 4),(32, 17)] - [(4, 4),(32, 12)]`

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

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

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

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

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

`=>` 5a = 5 and 5b = 50

`=>` a = 1 and b = 10