<h4>Zadaci - Matrice</h4> (a) Neka su

A = [\begin{matrix} § § V 1 (2, 4, 1) § § & § § V 2 (3, 5, 1) § § \\ § § V 3 (1, 3, 1) § § & § § V 4 (4, 6, 1) § § \end{matrix}]

B = [\begin{matrix} § § V 5 (5, 7, 1) § § & § § V 6 (- 1, 1, 0.5) § § \\ § § V 7 (2, 4, 1) § § & § § V 8 (0, 2, 0.5) § § \end{matrix}]

. Izračunajte

A + B

A - B

. (b) Zadane su matrice

C = [\begin{matrix} § § V 9 (3, 5, 1) § § & § § V 10 (2, 4, 1) § § \\ § § V 11 (- 1, 1, 0.5) § § & § § V 12 (6, 8, 1) § § \end{matrix}]

D = [\begin{matrix} § § V 13 (4, 6, 1) § § & § § V 14 (1, 3, 1) § § \\ § § V 15 (2, 4, 1) § § & § § V 16 (- 3, - 1, 0.5) § § \end{matrix}]

. Pomnožite matrice

C

D

i zatim izračunajte inverz matrice

C^{- 1}

. (c) Razmotrite matrice

E = [\begin{matrix} § § V 17 (1, 3, 1) § § & § § V 18 (2, 4, 1) § § \\ § § V 19 (3, 5, 1) § § & § § V 20 (4, 6, 1) § § \end{matrix}]

F = [\begin{matrix} § § V 21 (0, 2, 0.5) § § & § § V 22 (5, 7, 1) § § \\ § § V 23 (- 2, 0, 0.5) § § & § § V 24 (1, 3, 1) § § \end{matrix}]

. Napišite matricu

E F

i izračunajte

det (E F)

. (d) Neka je

G = [\begin{matrix} § § V 25 (2, 4, 1) § § & § § V 26 (- 1, 1, 0.5) § § \\ § § V 27 (3, 5, 1) § § & § § V 28 (0, 2, 0.5) § § \end{matrix}]

. Pronađite vlastite vrijednosti i odgovarajuće vlastite vektore za matricu

G

. (e) Zadane su matrice

H = [\begin{matrix} § § V 29 (2, 4, 1) § § & § § V 30 (4, 6, 1) § § \\ § § V 31 (- 1, 1, 0.5) § § & § § V 32 (3, 5, 1) § § \end{matrix}]

I = [\begin{matrix} § § V 33 (1, 3, 1) § § & § § V 34 (- 2, 0, 0.5) § § \\ § § V 35 (3, 5, 1) § § & § § V 36 (0, 2, 0.5) § § \end{matrix}]

. Provjerite jesu li matrice

H

I

jednake. (f) Funkcija

p (x)

definirana je kao

p (x) = [\begin{matrix} § § V 37 (1, 3, 1) § § \\ § § V 38 (2, 4, 1) § § \end{matrix}]

. Izračunajte

J^{K}

(J na potenciju K). (g) Uzmimo matrice

L = [\begin{matrix} § § V 39 (2, 4, 1) § § & § § V 40 (1, 3, 1) § § \\ § § V 41 (- 3, - 1, 0.5) § § & § § V 42 (0, 2, 0.5) § § \end{matrix}]

M = [\begin{matrix} § § V 43 (3, 5, 1) § § \\ § § V 44 (2, 4, 1) § § \end{matrix}]

. Pomnožite matricu

L

i vektor

M

te odredite rezultirajući vektor. (h) Matrica

N = [\begin{matrix} § § V 45 (1, 3, 1) § § & § § V 46 (2, 4, 1) § § & § § V 47 (3, 5, 1) § § \\ § § V 48 (4, 6, 1) § § & § § V 49 (5, 7, 1) § § & § § V 50 (6, 8, 1) § § \\ § § V 51 (7, 9, 1) § § & § § V 52 (8, 10, 1) § § & § § V 53 (9, 11, 1) § § \end{matrix}]

je kvadratna matrica reda 3. Izračunajte determinantu matrice

N

. (i) Neka je

P = [\begin{matrix} § § V 54 (2, 4, 1) § § & § § V 55 (- 1, 1, 0.5) § § \\ § § V 56 (1, 3, 1) § § & § § V 57 (3, 5, 1) § § \end{matrix}]

. Pronađite inverz matrice

P^{- 1}

. (j) Razmotrite matricu

Q = [\begin{matrix} § § V 58 (4, 6, 1) § § & § § V 59 (1, 3, 1) § § \\ § § V 60 (- 2, 0, 0.5) § § & § § V 61 (3, 5, 1) § § \end{matrix}]

. Odredite vlastite vrijednosti i odgovarajuće vlastite vektore za matricu

Q

.