Ais a 4x4 matrix and a^2 + 4a - 5i = 0. if det(a+2i)> 0, enter det(a+2i)

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Ответ:

Redmondwllc3439

14.01.2022

Mathematics

$\mathbf A^2+4\mathbf A-5\mathbf I=0$
$\implies\mathbf A^2+4\mathbf A+4\mathbf I=(\mathbf A+2\mathbf I)^2=9\mathbf I$
$\implies\det\bigg((\mathbf A+2\mathbf I)^2\bigg)=\det(9\mathbf I)$
$\implies\det(\mathbf A+2\mathbf I)^2=9^4\det\mathbf I$
$\implies\det(\mathbf A+2\mathbf I)=\pm\sqrt{9^4}$
$\implies\det(\mathbf A+2\mathbf I)=9^2=81$

where we take the positive root because we're told that the determinant is positive.

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Ответ:

OGxSniperGodx

09.02.2020

Mathematics

The answer to your question is: {y | y = –7, –1, 0, 9}

Step-by-step explanation:

Range is given by the dependent variable "y".

So, according to the information given, range must be 9,0, -7 and -1

or -7, -1, 0 , 9.

The second option.

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