Question

two of the eigenvalues of 3×3 matrix whose determinant is equal to 4 are -1 and 2 the third eigen value of the matrix is equal to​

Answer 1

SOLUTION

GIVEN

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

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