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Use the accompanying figure to write each vector listed in Exercises 7 and 8 as a linear combination of $\mathbf{u}$ and $\mathbf{v} .$ Is every vector in $\mathbb{R}^{2}$ a linear combination of $\mathbf{u}$ and $\mathbf{v} ?$Vectors $\mathbf{w}, \mathbf{x}, \mathbf{y},$ and $\mathbf{z}$

Each vector is a linear combination of $u + v$ since:$w = - u + 2 v$$x = - 2 u + 2 v$$y = - 2 u + 3.5 v$$z = - 3 u + 4 v$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

Jeff S.

September 16, 2021

Can you record this again with a working microphone? It's so difficult to understand with the messed up microphone

Missouri State University

Harvey Mudd College

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

01:28

Use the accompanying figur…

04:42

In Exercises $1-8,$ use th…

00:29

Write each vector as a lin…

01:41

03:54

For each pair of vectors $…

01:42

03:42

01:53

05:13

00:25

Okay, so for probably eight, we need to observe the the bigger in our next move. Eyes. I'm not people to allow the entire figure on this white board, but how to try to explain how, uh how do how do we sum problem? So first we need to find out. How do we defuse W in terms of U. N. V. So every review we observed the program involved in W, then we will find to be and some of to be a you, we'll be vast action. And for that tracks and again, we need to find out the andi be corresponding her low crime. So this will be to you and for us to be, because the negative to you and the to be will be the happens off a corresponding parallelogram and why it's over. Why, it will be, um, half off the so we first still have next to you. But, um, for V, we can take two in the two plus half. So that's 3/2 be. So that's why Oh, wait. I'm sorry. Three should be three plus one house. That is 7/2. Yes, I'm unhappy. Okay. And for her vectors, I'm dizzy. So the course woman in parallelogram. I observed the graft. It will be for a fee. Yeah, for a fee. Plus three of you. So it's minus three. Open. Thank you. So here's how are you?

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In mathematics, the absolute value or modulus |x| of a real number x is its …

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