Let be a vector space, and be two endomorphisms over . Denote by and the set of eigenvalues of and . Among the following claims, which one is correct?

Consider the following matrix:

Among the following values, which one is an eigenvalue of ?

Consider the matrix .

Let be endomorphism and a basis of .

Given that ,

what is the matrix associated to in the basis ?

Careful : in this question, checking wrong answers will yield negative points!

Consider the linear map whose associated matrix in the canonical bases is

Among the claims below, choose all the correct ones.

Let be the matrix

Which of the matrices below corresponds to ?

Careful : in this question, checking wrong answers will yield negative points!

Let be a linear map.

Among the following claims, choose all the correct ones.

Careful : in this question, checking wrong answers will yield negative points!

Let and be two finite dimensional vector spaces, a linear map, and two bases of and respectively. You are given

.

Among the following claims, choose all the ones that are correct.

Compute the following determinant

Let be a square matrix with 3 rows and 3 columns. Consider . Knowing that , what is the value of ?