6. Let A: =

-3 5 -5

-7 9 -5 and AER be a scalar.

-7 7-3

5

-3-A

-7

We can create a new matrix A - XI =

9-X

-5

-7

7

-3-X

Calculate det(A - XI) and then find all values of X € R for which the determinant

of det (A - XI) is 0. (Hint: Perform row operations R₂ - R₁ and column operations

C₁ + C₂ ).