Question

The eigen values of the matrix A are 2,3,5. Then the eigen values of adj A are

Answer 1

SOLUTION

GIVEN

The eigen values of the matrix A are 2,3,5

TO DETERMINE

The eigen values of adj A

CONCEPT TO BE IMPLEMENTED

$\sf{If \: \lambda_1, \lambda_2, \lambda_3, \: are \: the \: eigen \: values \: of \: a \: matrix \: A}$

Then the eigen values of adj A are given by

$c {\lambda_1}^{ - 1}, c {\lambda_2}^{ - 1}, c {\lambda_3}^{ - 1} \: \: where \: \: c =\lambda_1 \lambda_2\lambda_3$

EVALUATION

Here it is given that the eigen values of the matrix A are 2,3,5

We have to find the eigen values of adj A

Now product of eigen values

$c = 2 \times 3 \times 5 = 30$

So the the eigen values of adj A

$= 30 \times {2}^{ - 1} \: , \: 30 \times {3}^{ - 1} \: , \: 30 \times {5}^{ - 1}$

$\displaystyle = 30 \times \frac{1}{2} \: , \: 30 \times \frac{1}{3} \: , \: 30 \times \frac{1}{5}$

$= 15\: , \:10 \: , \:6$

FINAL ANSWER

The eigen values of the matrix A are 2,3,5. Then the eigen values of adj A are 15 , 10 , 6

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