Question
Asked Oct 25, 2019
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Use the determinant to find 4heValues
(k for..
Ax X
Such that
3
2 1
A=
7
c)
S
-3
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Use the determinant to find 4heValues (k for.. Ax X Such that 3 2 1 A= 7 c) S -3

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Step 1

To find the eigenvalues of the given matrices using determinant conidition (equation)

Step 2

The determinant condition is for the homogenous system to have non-zero solutions

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Notation : use c instead of a 1 Re quired c with a)A = 5 2 1-с 6 х х х А = C 5 2 c 0 У у Г1-с det 5 0 х with = 0 2-c 1 у 5(1-с)(2-с)- 30 %3D 0 с-Зс - 28 %3 0 (c-7)(c+4) 0; so,c 7,-4

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Step 3

b) proceeding just as in a) we find ...

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7 b)A = -3 Required c with -1 7-c det -3 -1-c 4 =0 (7-e-c)+12 = 0 c2-6c5= 0 (c5)(c-1) 0; so,c 5,1

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