Question

If `A=[(3,-2),(4,-1)]`, then find all the possible values of `lambda` such that the matrix `(A-lambdaI)` is singular.

Answer 1

Correct Answer - `1 pm 2i`
We have
`(A-lambda I)=[(3,-2),(4,-1)]-lambda [(1,0),(0,1)]`
`=[(3-lambda,-2),(4,-1-lambda)]`
`(A-lambda I)` is singular.
`:.` det. `(A-lambda I)=0`
`implies )3-lambda) (-1-lambda)-(-2) 4=0`
`implies lambda^(2)-2lambda+5=0`.
`implies lambda=1 pm 2i`