17.01.05

RE-ASSESSMENT TEST 2

FULL NAME:

Task1. (8 p.) Solve the following matrix equation : 2 AX = B,

for
,
.

Task 2. (7 p.) Check whether the set
is a linear subspace of R³.

Task 3. (12 p.) Find the relationship between the value of parameter a and the number of solutions of the system

Task 4. (7 p.) Define the linear independence of vectors and check whether the following vectors are linearly independent:
.

What is the dimension of the space V spanned by these vectors? Is V = R⁵ ? Justify your answer.

Task 5. (8 p.) Determine whether the vectors
produce a basis of space R³. Present , if it is possible , vector u = (0, 0, 0) as two different linear combinations of vectors
.

Task 6. (8 p.) Calculate the determinant

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