B

28.XI.05

TEST 1

Full name in CAPITAL BLOCK LETTERS .....................................................................

Task 1 Write the exponential form of

Task 2 Find all the complex roots of the polynomial

,

and determine their real and imaginary parts.

Task 3 Sketch, by shading the appropriate area of the complex plane, the set

.

Task 4 Find the rank of

Task 5 Solve the following system of equations using the Gaussian elimination method,

Task 6 Find all the solutions of the following system of equations

Justify your answer using the Kronecker-Capelli Theorem.

Task 7 Determine, if it is possible, the elements of the matrix M, if

where I is the identity matrix,
,
,

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