Let and be two vector spaces, and two linear maps. Moreover, suppose that . Among the following claims, which one is the correct one? (only one possible answer)

Consider the linear map defined by .

Give the dimension of .

Let be a vector space, , and three bases of and an endomorphism over . Among the following claims, which ones are correct?

Careful: any wrong answer will yield negative points.

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

Let be a vector space, and be two bases of . Which of the following is a correct definition of the matrix ?

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 ?

Let be the matrix

Among the matrices below, which one corresponds to ?

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.