Ushtrimi 13 | Vlerësim 7 | Matematika 10 - 11: Pjesa II | Zgjidhje Ushtrimesh

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Jepen vektorët $\vec{x}=\dbinom{4}{1}$ , $\vec{y}=\dbinom{7}{-2}$ dhe $\vec{z}=\dbinom{-8}{5}$ . Shkruani vektorët e mëposhtëm.

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Zgjidhja

$3\vec{x}=3\dbinom{4}{1}$ $=\dbinom{3\times4}{3\times1}=$ $\dbinom{12}{3}$
$5\vec{y}=$ $5\dbinom{7}{-2}=$ $\dbinom{5\times7}{5\times(-2)}=$ $\dbinom{35}{-10}$
$-2\vec{z}=-2\dbinom{-8}{5}=$ $\dbinom{(-2)\times(-8)}{(-2)\times5}=$ $\dbinom{16}{-10}$
$\vec{y}+\vec{z}=$ $\dbinom{7}{-2}+\dbinom{-8}{5}=$ $\dbinom{7+(-8)}{(-2)+5}=$ $\dbinom{-1}{3}$
$\vec{y}-\vec{x}=$ $\dbinom{7}{-2}-\dbinom{4}{1}=$ $\dbinom{7-4}{(-2)-1}=$ $\dbinom{3}{-3}$
$\vec{x}+\vec{y}+\vec{z}=$ $\dbinom{4}{1}+\dbinom{7}{-2}+\dbinom{-8}{5}=$ $\dbinom{4+7+(-8)}{1+(-2)+5}=$ $\dbinom{3}{4}$
$4\vec{z}-2\vec{x}=$ $4\dbinom{-8}{5}-2\dbinom{4}{1}=$ $\dbinom{4\times(-8)-2\times4}{4\times5-2\times1}=$ $\dbinom{-32-8}{20-2}=$ $\dbinom{-40}{18}$
$4\vec{y}+3\vec{x}-2\vec{z}=$ $4\dbinom{7}{-2}+3\dbinom{4}{1}-2\dbinom{-8}{5}=$ $\dbinom{4\times7+3\times4-2\times(-8)}{4\times(-2)+3\times1-2\times5}=$ $\dbinom{28+12+16}{-8+3-10}=$ $\dbinom{56}{-15}$
$3\vec{z}-(\vec{x}+\vec{y})=$ $3\dbinom{-8}{5}-(\dbinom{4}{1}+\dbinom{7}{-2})=$ $\dbinom{3\times(-8)}{3\times5}-(\dbinom{4+7}{1+(-2)})=$ $\dbinom{-24}{15}-\dbinom{11}{-1}=$ $\dbinom{-24-11}{15-(-1)}=$ $\dbinom{-35}{16}$