matrices

Question

Let A be a real $2 \times 2$ matrix.If $5 + 3\iota$ is an eigen value of A, then det(A)

(A)equals 4

(B)equals 8

(C)equals 16

Answer 1

Using the eigen value properties, it is known that complex eigen values are present in conjugates. So, if one eigen value is 5+3i, other must be 5-3i. Also from the eigen value properties, the product of the eigen values is equal to the determinant of the matrix. Thus for a 2x2 matrix, two eigen values: 5+3i, 5-3i.

So, (det A) = (5+3i)*(5-3i) = 25 + 9 = 34.

Comments

I think (a+b)(a-b) = a^2 - b^2

 (det A) = (5+3i)*(5-3i)

            = 25 - 9i^2

        since, i^2 = -1

             = 25 -(-9)

             =34

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yes, Answer should be 34.

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Aspirant Please check solution properly before selecting.