Question

If the eigen values of a matric A are 2,3,7 then the determinant of the matrix A is

Answer 1

SOLUTION

GIVEN

The eigen values of a matrix A are 2 , 3 , 7

TO DETERMINE

The value of the determinant of the matrix A

EVALUATION

We know that :

• The sum of the eigen values of A is the same as the trace of A

• The product of the eigen values of A is the same as the determinant of A.

Now it is given that the eigen values of a matrix A are 2 , 3 , 7

Thus the required value of the determinant of the matrix A

= Product of the eigen values of A

= 2 × 3 × 7

= 42

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