Question

Given A = `[(p, 0),(0, 2)]`, B = `[(0, -q),(1, 0)]`, C = `[(2, -2),(2, 2)]` and BA = C². Find the values of p and q.

Answer 1

Given: A = `[(p, 0),(0, 2)]`, B = `[(0, -q),(1, 0)]`, C = `[(2, -2),(2, 2)]` and BA = C²

Now BA = `[(0, -q),(1, 0)][(p, 0),(0, 2)]`

= `[(0 xx p + (-q) xx 0, 0 xx 0 + (-q) xx 2),(1 xx p + 0 xx 0, 1 xx 0 + 0 xx 2)]`

= `[(0 + 0, 0 - 2q),(p + 0, 0 + 0)]`

= `[(0, -2q),(p, 0)]`

And C² = C × C

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

= `[(2 xx 2 + (-2) xx 2, 2 xx (-2) + (-2) xx 2),(2 xx 2 + 2 xx 2, 2 xx (-2) + 2 xx 2)]`

= `[(4 - 4, -4 - 4),(4 + 4, -4 + 4)]`

= `[(0, -8),(8, 0)]`

∵ BA = C²

∴ `[(0, -2q),(p, 0)]= [(0, -8),(8, 0)]`

Comparing the elements; –2q = –8

`\implies q = (-8)/(-2) = 4`

p = 8

Hence p = 8, q = 4