Question

Two of the eigen values of a 3 order matrix whose determinant equals 4 are 1 and 2,then third eigen value is _______.

Answer 1

Step-by-step explanation:

Two of the eigen values of 3×3 matrix whose determinant is equal to 4 are -1 and 2

TO DETERMINE

The third eigen value of the matrix

CONCEPT TO BE IMPLEMENTED

The product of the eigen values of a square matrix A is det A

EVALUATION

Here it is given that two of the eigen values of 3×3 matrix whose determinant is equal to 4 are -1 and 2

Let c be the third eigen value of the matrix

Now we know that the product of the eigen values of a square matrix A is det A

So

c × ( - 1 ) × 2 = det A

⇒ - 2c = 4

⇒ c = - 2

FINAL ANSWER

Hence the required third eigen value of the matrix = - 2

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Answer 2

Answer:

Third eigen value is 2.

Step-by-step explanation:

Given two eigen values of a matrix A of order 3 are 1 and 2.

Determinant of matrix A, detA = 4.

Let the third eigen value = x

We know that the product of eigen values of a square matrix is equal to the determinant of that matrix.

So, 1 × 2 × x = 4

      2 × x = 4

      x = 2

Thus, the third eigen value is 2.