For the matrix `A= [[3,2],[1,1]]`, find the numbers a and b such that `A^2+aA+bI=0.`

Explanation

`A = [[3,2],[1,1]]`

`:. A^2 = [[3,2],[1,1]] [[3,2],[1,1]] = [[9+2,6+2],[3+1,2+1]] = [[11,8],[4,3]]`

`aA = a [[3,2],[1,1]] = [[3a,2a],[a,a]]`

`bI = b[[1,0],[0,1]] = [[b,0],[0,b]]`

`:. A^2-aA+bI = [[11,8],[4,3]]+[[3a,2a],[a,a]]+ [[b,0],[0,b]] `

It is given that `A^2-aA+bI = 0`

`:. [[11,8],[4,3]]+[[3a,2a],[a,a]]+ [[b,0],[0,b]] = [[0,0],[0,0]]`

`=>11+3a+b = 0 => 3a+b = -11->(1)`

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