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Use the vector $\mathbf{u}=\left(u_{1}, \ldots, u_{n}\right)$ to verify the following algebraic properties of $\mathbb{R}^{n}$ .a. $\mathbf{u}+(-\mathbf{u})=(-\mathbf{u})+\mathbf{u}=0$b. $c(d \mathbf{u})=(c d) \mathbf{u}$ for all scalars $c$ and $d$

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Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

05:49

Use the vectors $\mathbf{u…

00:59

For the arbitrary vectors …

01:57

01:54

01:01

Let $\mathbf{u}=\langle a,…

00:29

01:06

03:12

02:01

02:21

Okay, so for problem 34 were given. Vector, you, Coordinator is with you one. You too. Two you in. And the first property we need to verify is, um say first part, eh? Is you? Thus negative view is you go to a necktie, view us you, which is equal to zero. So the first relationship is very easy to verify, right? We first just to observe elective you is negative. You want connective You too, until elective you in. So by adding the coordinate coordinates directly next you class, you will just be 000 till zero. There are in zeros here, which is the same as you first active you, which is sterile. Okay. And the second second relationship we need to identify is given to scale. Er's cnt We want to show that C times t that's you. Is this the same as the product off? We, uh, product of CD calculated first times. You so here we we started from the life inside. First, consider you d times you So this will get de times you want to the times u n And then we won't buy Buy another skater. See? So c t u This will be C d you want till C D u N. Now. Right now we can You can see that this three I'll just use of record two separated separate them this CD and you are all numbers so we can put the brackets infront off so we can use bracket to take out to sea to capitalise e de pers. So that's actually see times d 10 times you till c times t times you eh Okay, so now we can take out the product of CD He brought off the vector so that seedy times you want two u. N and this is CD times better you

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