Question

A is an singular matrix of order3 ,2and 3 are the eigen values.find the third eigen value

Answer 1

The third eigen value = 0

Given :

• A is an singular matrix of order 3

• 2and 3 are the eigen values

To find :

The third eigen value

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that A is an singular matrix of order 3

2and 3 are the eigen values

Step 2 of 2 :

Find third eigen value

It is given that A is a singular matrix

⇒ det A = 0

Now two given eigen values are 2 & 3

We know that the determinant is the product of the eigenvalues.

So product of the three eigenvalues = 0

Since two given eigenvalues are non zero

Hence third eigenvalue must be zero

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