Question

Consider the matrix A=(3 −2).

(4 −1)
Then all possible values of λ such that the determinant of B=A−λI is 0, where I=(1 0) and i=√−1.
(0 1)
A. 1±2i
B. 2±3i
C. 3±4i
D. 5±6i

Answer 1

The possible values of λ in the given equation are 1 ± 2i. So the correct answer is option A.

Step-by-step explanation:

The matrix A is given as A = (3 -2) (4 -1). We need to find all possible values of λ such that the determinant of B = A-λI is 0, where I = (1 0) and i = √-1.

To find these values, we can set up the equation det(B) = 0 and solve for λ.

By substituting the values of A and I into the equation and simplifying, we get a quadratic equation. Solving this equation will give us the possible values of λ.

The possible values of λ are 1 ± 2i.