Let `A=[[a,b],[c,d]]` be a `2xx2` real matrix. If `A-alphaI` is invertible for every real number `alpha` , then

Let `A=[[a,b],[c,d]]` be a `2xx2` real matrix. If `A-alphaI` is invert

1.	Let `A=[[a,b],[c,d]]` be a `2xx2` real matrix. If `A-alphaI` is invertible for every real number `alpha` , then
Answer» `A-alpha*I=[[a,b],[c,d]]-[[alpha,0],[0,alpha]]` `=[[a-alpha,b],[c,d-alpha]]` `=(a-alpha)(d-alpha)-bc!=0` `alpha^2-alpha(a+d)+ad-bc` `(a+d)^2-4(ad-bc)<0`

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Let `A=[[a,b],[c,d]]` be a `2xx2` real matrix. If `A-alphaI` is invertible for every real number `alpha` , then

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