Question

1. Find the sum and product of the eigenvalues of -2 2 -3
2 1 -6
-1 -2 0 without calculating them.​

Answer 1

Answer:

sum = -1

product = 25

Step-by-step explanation:

sum would be trace of the matrix

and product would be determinant of matrix

Answer 2

Answer:

The sum of the eigenvalues is $-1$ and the product is 45

Step-by-step explanation:

Tip:

• The Sum of the Eigenvalue is a trace of a matrix.
• The product of the Eigenvalue is the determinant of the matrix.

Step 1 of 2: Finding the Sum

• Given matrix is

      $\left[\begin{array}{ccc}-2&2&-3\\2&1&-6\\-1&-2&0\end{array}\right]$  

• The sum of the Eigenvalue is equal to the sum of the diagonal elements i.e. trace
• $Sum= -2+1+0 =-1$

Step 2 of 2: Finding the Product

• The product of the Eigenvalue is the determinant of the matrix.

• The determinant is given by

        $\det A =-2(0-12)-2(-6)-3(-4+1)$

                  $=24+12+9\\=45$