PN2a

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.) Show that the vectors
form a basis of
. Find the coordinates of vector
relative to this basis.

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

.

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