PN2b

TEST 2

Task 1. (8 p.) Using elementary row operations find the inverse of matrix

Task 2. (7 p.) Find the rank of matrix A and give an example of the largest non-zero minor.

.

Task 3. (12 p.) Find the dependence of the number of solutions of the following system of equations, on the value of parameter a

.

Task 4. (7 p.) Find a basis and the dimension of the linear space
.
Is
?

Task 5. (8 p.) Let
Determine a vector
such that vectors


constitute a basis for
and that the coordinates of vector
relative to this basis are
.

Task 6. (8 p.) Determine a basis for the solution space of the following system of equations

.

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