For the matrix , find the numbers a and b such that A 2 + aA + bI = O.

Question

Philoid · Accepted Answer

We have A² = A.A =

Since A² + aA + bI =

So A² + aA + bI =

Hence 10+3a+b = 0 …(i)

5+a = 0 …(ii)

5+2a+b = 0 …(iii)

From (ii) a = -5

Putting a in (iii) we get b = 5

So a = -5 and b = 5 satisfy the equation.

For the matrix , find the numbers a and b such that A2 + aA + bI = O.