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Let D= [ array lll 1 & 0 & 0 0 & 2 & 0 0 & 0 & 3 array ] and P= [ array lll 7 & 0 & 2 0 & 1 & 0 2 & 0 & 5 array ] . Consider A=P⁻¹ D P . Find det. (A^2+A ) .

Correct answer

144

Step-by-step solution

det (A^2+A )= det [ (P⁻¹ D P ) (P⁻¹ D P )+P⁻¹ D P ] or det (P⁻¹ D^2 P+P⁻¹ D P ) or det (P⁻¹ (D^2+D ) P ) or det (P⁻¹ P ) det (D^2+D ) or or det (I) det (D) det .(D+I)1^3 (1 2 3) (2 3 4)=6 24=144

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