ALG k1a sydow 04 11 22 A

22.11

TEST 1

A

Fuli Name:

Find an integer x which satisfies the following congruence 4x=3(mod 23).

Are there any morę such numbers? Justify your answer. If it is possible give the generał formula for such numbers.

>2- The complex number 2i is a root of the polynomial x' + 6x ⁴ + 15*³ + 30x² +44x + 24. Find all the other roots.

\

3. Find the value of

\4. Knowing that

-S

+ 7

1-7

and write the result in trigonometric form.

+ l+/'VlO-2V5

	f	fi 1		f^1
4	cos	— 71	+ / sin	-71
		U J		U JJ

write the following numbers in exponential form:    V5 +1 - /v 10 - 2 J5 ,

-(V5+l) + /'VlO-2V5 -(V5 + l)-/'VlO-2V5 .

5. Give the geometrical interpretation of the following system (sketch the set):

0 < argz < —7t i    4

„    „    , Present the vertexes of the obtained figurę as complex numbers.

[2 < Rez < 4    ^&    F

■4r a) Solve the eąuation 2(3^ + X)- I +4H -3A = X , where A =

and / is the identity matrix.

b) Calculate the product AX‘ .

2    3

-4    1

B =

1 1 1 0

1 2 2 4 2 6

J	3
6	9
7	6

to row echelon

<1. Using elementary row operations reduce the matrix A =

form. Find the rank of A, justify your answer.