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In Exercises 23 and $24,$ mark each statement True or False. Justify each answer.a. Another notation for the vector $\left[\begin{array}{r}{-4} \\ {3}\end{array}\right]$ is $\left[\begin{array}{cc}{-4} & {3}\end{array}\right]$ andb. The points in the plane corresponding to $\left[\begin{array}{r}{-2} \\ {5}\end{array}\right]$ and$\left[\begin{array}{r}{-5} \\ {2}\end{array}\right]$ lie on a line through the origin.c. An example of a linear combination of vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$is the vector $\frac{1}{2} \mathbf{v}_{1}$ .d. The solution set of the linear system whose augmentedmatrix is $\left[\mathbf{a}_{1} \quad \mathbf{a}_{2} \quad \mathbf{a}_{3} \quad \mathbf{b}\right]$ is the same as the solutionset of the equation $x_{1} \mathbf{a}_{1}+x_{2} \mathbf{a}_{2}+x_{3} \mathbf{a}_{3}=\mathbf{b} .$e. The set $\operatorname{Span}\{\mathbf{u}, \mathbf{v}\}$ is always visualized as a planethrough the origin.

FALSE, FALSE, TRUE, TRUE, FALSE

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

Oregon State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

06:43

In Exercises 23 and $24,$ …

09:01

In Exercises 21 and $22,$ …

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In Exercises 19 and $20,$ …

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In Exercises 19 and 20, V …

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In Exercises 21 and 22, ma…

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Mark each statement True o…

08:43

14:16

In Exercises 17 and $18,$ …

03:53

In Exercises 25 and $26, A…

01:35

okay. In this question, there's a set off five questions from A to E. And we have to find that these statements are true or false so fast, The statement is the question is another notation off the vector minus 43 is is minus 43 Okay, so it is false because vectors are represented as call the metrics is okay. And this is two dimensional, two dimensional vector. And this is set off toe one dimensional mattress mattresses. Okay, two dimensional vectors. So this is false. How come Toby be the caution be is the points in the plane corresponding toe minus 25 and minus five to lie on a line through the origin. Okay, so you will check that this past for the reason or not So minus two and five is hair. So this will be the line and minus five. And who will be here? So this will be line, and it does not pass to the or is not. So it is false. Okay, now we should see an example off a linear combination of vector even. And we do. Is Victor halfway one? Okay, so we can say that a linear combination is defined as the sum of vector. We won we 233 and so on We end multiplied by these killers C one c two c three, as seen So so. Therefore, as for the ocean half even Okay, so half even is a linear combination is a linear combination. How? Because it is the same value off half, even plus zero. Well, okay, here's even is even toe half and sit close to zero. So this statement is true. Okay, now the caution be on the day The solution set off Linear system has documented metrics is a one a two a three b has the same solution. Seems as the solution set off equation Excellent even plus x two, a two plus x 383 equals to be so. Yes, it is true. Why? Because the solution says are saying because the augmented metrics off this equation is even a two, a three and b So this solution off this documented metrics and because they are same, then the solution will be also same. So this will be true and the last one e the sad span you ve is always visualized as a plane through the reason is always we realize as plain through the or reason and this is false. Why? Because if these factors are linearly dependent, then they respond. Will be will produce a line. Okay, note a plane so line will be correct. Plane will be not correct hands. The statement is false. So we have the final answers here. A false B false see True D Do you on e false? So this will be our final answer. Thank you.

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