Question

Let A be a 3×3 matrix with real entries such that det(A)=6 and tr(A)=0. If det(A+I)=0 (I denotes 3×3 identity matrix), then the eigen values of A



please do each and every step
I want step by step solution
please...​

Answer 1

Step-by-step explanation:

$It \: is \: much \: simpler \: than \: this$

$det(A+I)=0det(A+I)=0 </p><p>$

$means \: that \: one \: of \: the \: eigenvalues$

$must \: be \: equal \: - 1 \\ so \: without \: loss \: of \: generality \: we \:$

$can \: a = - 1 \\ \: the \: other \: two \: bits \: of \: information \:$

$so \: bc = - 6 \: \\b + c = 1 \\ so \: a = - 1 \\ b = - 2 \\ c = 3$

$Check \: the \: following \: \\ \\ for a 3×3 matrix AA, and \: putting Δ:=detA \\ \\ T:=tr.AΔ = det,T:=tr.A , we have that its characteristic polynomial is</p><p></p><p>x3−Tx2+(T2−tr.(A2))x−Δ</p><p></p><p>$