Question 1 (1 point) Saved Let u⃗ =

Question 1 (1 point) Saved Let $\vec{u} = \begin{bmatrix} 1 \\ 1 \\ -1 \end{bmatrix}$ and $\vec{v} = \begin{bmatrix} 2 \\ -2 \\ 0 \end{bmatrix}$. Which one of the following vectors is a linear combination of $\vec{u}$ and $\vec{v}$?

Transcript

00:01 So in this problem, we're given these three vectors, u, v, and w, where u is 1 -1 -2, v is negative 2 -3 -1, and w is 2 -9 -1.

00:12 And we're asked to determine in a set of vectors here, which ones are linear combination of u -v -w.

00:45 Let's look for a second at the z.

00:53 Look at the z component.

01:00 All right.

01:02 So if we do, then we have the z is.

01:09 So you notice that w, it's 2 negative 1 -1, right? okay.

01:29 And in u, it's 1 -1 -2.

01:40 V, it's negative 2 -3 -1.

01:42 All right.

01:43 So we can set this up.

01:45 As two times the sum of the x components which will be x plus okay so let's let's look for a second let's take that off if we look at the z component for each one of these what do we notice in u in the vector u we notice that x plus y is z one plus one equals two okay what about in v again we got x plus y because we get negative two plus three is equal to one and look at it in w it's x plus y as well two minus one is one okay so any linear combination will have z is equal to to x plus y.

03:30 No matter how we add these three together, no matter what we multiply them by and all, it's still going to have that relationship happen in it.

03:39 So let's now look at the points that are given.

03:43 So 0 -1 -1.

03:47 Well, x plus y is 0 plus 1, which is 1, which is not equal to 0.

03:57 So not that one.

04:02 Let me put it this way.

04:04 Let me say not.

04:08 Okay.

04:10 Then let's look at 1 -0 -0.

04:14 Again, x plus y...

Question

Question 1 (1 point) Saved Let $\vec{u} = \begin{bmatrix} 1 \\ 1 \\ -1 \end{bmatrix}$ and $\vec{v} = \begin{bmatrix} 2 \\ -2 \\ 0 \end{bmatrix}$. Which one of the following vectors is a linear combination of $\vec{u}$ and $\vec{v}$?

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