Answer to Question #200625 in Linear Algebra for Vina

Question

Let ~u =< 3, −1, −2 >, ~v =< −1, 0, 2 > and w~ =< −6, 1, 4 >.

Compute the expressions below.

(2.1) ~v + 3w~

(2.2) 3~u − 2~v

(2.3) −(~v + 3~u).

Answer 1

(2.1)

$$\vec v+3\vec w=\langle-1+3(-6), 0+3(1), 2+3(4)\rangle$$

$$\vec v+3\vec w=\langle-19, 3, 14\rangle$$

(2.2)

$$3\vec u-2\vec v=\langle3(3)-2(-1), 3(-1)-2(0), 3(-2)-2(2)\rangle$$

$$3\vec u-2\vec v=\langle11, -3, -10\rangle$$

(2.3)

$$-(\vec v+3\vec u)=\langle-(-1+3(3)), -(0+3(-1)), -(2+3(-2))\rangle$$

$$-(\vec v+3\vec u)=\langle-8, 3, 4\rangle$$