Question

For a given matrix A of order 3,|A| = 32 and two of its Eigen values are 8 and 2 find
the sum of the Figen Values​

Answer 1

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Answer 2

The sum of the Eigen values = 12

Given :

• For a given matrix A of order 3 , |A| = 32

• Two of its Eigen values are 8 and 2

To find :

The sum of the Eigen values

Solution :

Step 1 of 2 :

Find third eigen value

Here it is given that for a given matrix A of order 3 , |A| = 32

Two of its Eigen values are 8 and 2

We know that the determinant is the product of the Eigen values.

Since A is a matrix of order 3

So A has three eigen values

Thus we get

Product of the three eigen values = | A |

⇒ 8 × 2 × Third eigen value = 32

⇒ 16 × Third eigen value = 32

⇒ Third eigen value = 2

Step 2 of 2 :

Find sum of the Eigen values

The three eigen values are 8 , 2 , 2

The sum of the Eigen values

= 8 + 2 + 2

= 12

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