laramath laramath

05-04-2017
Mathematics

contestada

If A is a 3 ×3 matrix and 5(A+I)=I. What is det(A+I) .

Respuesta :

LammettHash LammettHash

05-04-2017

[tex]5(\mathbf A+\mathbf I)=\mathbf I\implies \mathbf A=-\dfrac45\mathbf I[/tex]
[tex]\implies\det\mathbf A=\det\left(-\dfrac45\mathbf I\right)=\left(-\dfrac45\right)^3\det\mathbf I=-\dfrac{64}{125}[/tex]

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