A 30.01.07

Linear Algebra Examination

Full Name:

Group number:

Task 1 (20p.) Find the real and imaginary parts of the roots of:

.

Task 2 (18p.) Find the basis and dimension of the solution space of:

Task 3 (16p.) Find the basis for

S= Lin( (1,1,01), (1,-1,2,3), (2,0,2,4), (5,-1,6,11) ).

Find the coordinates of the vector v relative to the determined basis.

Task 4 (14p.) Find the real and imaginary parts Re z, Im z of
.

Task 6 (16p.) The linear transformation
is defined by

.

Find the eigenvalues and eigenvectors of this transformation. Do they constitute a basis for
? Can the matrix of L be written in diagonal form? If so, write this matrix.

Task 7 (16p.) Determine the relationship between the value of the parameter 'q' and the number of solutions of the following system of equations.

---