Question

if the sum of the two eigen values and trace of 3×3 matrix A is equal , find the values of |A|​

Answer 1

Answer:

if the sum of the two eigen values and trace of 3×3 matrix A is equal , find the values of |A|

Answer 2

If the sum of the two eigen values and trace of 3 × 3 matrix A is equal , then the value of |A| = 0

Given :

The sum of the two eigen values and trace of 3 × 3 matrix A is equal

To find :

The value of |A|

Solution :

Step 1 of 2 :

Find the third eigen value

Here it is given that sum of the two eigen values and trace of 3 × 3 matrix A

As we know that trace is the sum of the eigen values

So third eigen value is 0

Step 2 of 2 :

Find value of |A|

Now the value of |A|

= Product of the eigen values

= 0 [ As third eigen value is 0 ]

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