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In Exercises 23 and 24, mark each statement True or False. Justify each answer.a. Any list of five real numbers is a vector in $\mathbb{R}^{5}$ .b. The vector $\mathbf{u}$ results when a vector $\mathbf{u}-\mathbf{v}$ is added to the vector $\mathbf{v}$ .c. The weights $c_{1}, \ldots, c_{p}$ in a linear combination $c_{1} \mathbf{v}_{1}+\cdots+c_{p} \mathbf{v}_{p}$ cannot all be zero.d. When $\mathbf{u}$ and $\mathbf{v}$ are nonzero vectors, $\operatorname{Span}\{\mathbf{u}, \mathbf{v}\}$ contains the line through $\mathbf{u}$ and the origin.e. Asking whether the linear system corresponding to an augmented matrix $\left[\begin{array}{lll}{\mathbf{a}_{1}} & {\mathbf{a}_{2}} & {\mathbf{b}}\end{array}\right]$ has a solution amounts to asking whether $\mathbf{b}$ is in $\operatorname{Span}\left\{\mathbf{a}_{1}, \mathbf{a}_{2}, \mathbf{a}_{3}\right\}$

a. Trueb. TRUEc. Falsed. Truee. TRUE

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

Missouri State University

Campbell University

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

06:43

In Exercises 23 and $24,$ …

09:01

In Exercises 21 and $22,$ …

02:07

In Exercises 21 and 22, ma…

06:10

In Exercises 19 and 20, V …

05:09

In Exercises 19 and $20,$ …

03:53

In Exercises 25 and $26, A…

06:33

In Exercises 29 and $30, V…

07:24

In Exercises 25 and $26,$ …

01:35

In Exercises 17 and $18,$ …

08:43

Okay, so this question is set off Five question from A to E. And we have to justified that the statements are true or false. So off question is any list off five riel numbers is a vectoring are five. Any list off? Five riel numbers. Numbers is a veteran are five. Okay, we can say straight from the book that if is, and a positive in geezer positive and teacher are and the notes the collection off or lists off and riel numbers. Okay, so this definition comes straight from the textbook, and this is correct for N So if anyone's toe five, then five really numbers is a vector in our five, then a statement is drill. Okay. My question be the question be is caution be is the vector u is the result when a vector after U is the result When the vector u minus, we is added to the vector V. Okay, let's check it. Vector. You bless after u minus after we equals toe you. And that is correct because we know the submission and subsection of the vector on this'll will be. This is the okay. This will be simple. You victor, It was to you, Doctor. So this will be true. Okay, now question to the see and emotions he is. No. Wait C one c two c three or C p in a linear combination. See, even view on plus C two, e two and so on. CPP cannot be all zero. Okay, the question in the in the statement is these where it's even. C two c three cannot be. Cannot be zero. Okay, so there is no reason, no reason. Always it cannot be zero indeed. The span off. Any vectors content? Zero vector besides this. Besides this, there is no rule or no reason that all words cannot be zero. So this statement is false. Okay, Mouth fort on T and the caution D is Fendi is whether you and we are non zero vectors. OK, you and we are known. Zero actors unknown your of actors. Then they spend you. We contains the line through you and autism. Okay, So Okay, if you and we are non zero vectors in our three with we know the multiple off you, then they spend you Is the plane in artery Okay, this will be playing in are three and in this plan, there will be to line the first line and this plan directors contents, you vector, vector and zero. Okay. And there will be, Yes, one line that passes through you and back and zero or means a reason. And the other one is we and zero. Okay, so this statement is true. And now fifth in the fifth question is e discussion asking whether the linear system corresponding to undocumented metrics, even a to be as a solution, amounts to asking whether be is in a span, even a two and a three. And yes, it is true because a vector equation excellent even plus x +282 lasagne x n a n it was toe. He has the same solution. Same solution solution said as the linear system whose augmented metrics is even vector a vector a three vector So on a in vector and a solution will be be vector. So this statement is two. Okay, so we have the final answers. A true be also true See falls the true e chill. So this is your final answer. Thank you

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