10.01.05

TEST 2

Full Name and Group:

1. (12p) Find the values of the parameters a and b for which the set of solutions of the following system a) has one element , b) has an infinite number of elements, c) is empty.

3x - 2y + z = b

5x - 8y + 9z = 3

2x + y + az = -1

2. (7p) Solve the following matrix equation

3. (6p) Find the determinant

4. (7p) Is set W a linear subspace of R³,

?

5. (6p) Find the value a for which the vectors:

v₁ = (1,1,a), v₂ = (2,1,4), v₃ = (4,2,8)

are linearly independent.

6. (6p) Determine the dimension of the linear subspace

.

7. (6p) The coordinates of the vector a relative to the unit basis are (2,3). Find the coordinates of a relative to the basis: u=(1,1), v=(-1,3).

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