Question

if the eigenvalues of a matrix a of order 3 are 2,3 and 4. find the eigenvalues of adj A

Answer 1

Answer:

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Step-by-step explanation:

SOLUTION

GIVEN

Eigen values of A of order 3x3 are 2,3 and 1

TO DETERMINE

Eigen values of adjoint of A.

CONCEPT TO BE IMPLEMENTED

If \sf{ { \lambda}_{1}, {\lambda}_{2},..., {\lambda}_{n}}λ

1

,λ

2

,...,λ

n

are eigen values of a n × n non singular matrix A then the eigen values of adj A are

\sf{ { c{\lambda}_{1}}^{ - 1} , c{{\lambda}_{2}}^{ - 1} ,..., c{{\lambda}_{n}}^{ - 1} }cλ

1

−1

,cλ

2

−1

,...,cλ

n

−1

Where \sf{ c = { \lambda}_{1} {\lambda}_{2} \times ... \times {\lambda}_{n}}c=λ

1

λ

2

×...×λ

n

EVALUATION

Here it is given that Eigen values of A of order 3x3 are 2,3 and 1,

So the Eigen values of adjoint of A

= 2 × 3 , 3 × 1 , 2 × 1

= 6 , 3 , 2