Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Each statement in Exercises 33–38 is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is true, give a justification. (One specific example cannot explain why a statement is always true. You will have to do more work here than in Exercises 21 and 22.)If $\mathbf{v}_{1}, \ldots, \mathbf{v}_{4}$ are linearly independent vectors in $\mathbb{R}^{4},$ then $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ is also linearly independent. [Hint: Think about $x_{1} \mathbf{v}_{1}+x_{2} \mathbf{v}_{2}+x_{3} \mathbf{v}_{3}+0 \cdot \mathbf{v}_{4}=\mathbf{0} . ]$

True.

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 7

Linear Independence

Introduction to Matrices

Oregon State University

McMaster University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

02:42

Each statement in Exercise…

02:58

02:36

02:24

02:00

08:20

For the following exercise…

01:38

06:33

In Exercises 29 and $30, V…

03:54

Mark each statement True o…

00:41

In Exercises 148–155, dete…

in this video, we're gonna be solving problem number 38 from section 1.7, which is being some linear independence. So in this problem were given Ah, a statement which states that which gives us four backers everyone through before. Uh, sorry, uh gives us four vectors be won through before. And, um, it states that if the set of the one of the two of you three and before is linearly independent down the set of we won't be to envy three with a weight of zero on before, but because it's x excluded is also literally independent. So it asked us to consider this equation. This is basic. Just the next expanded form of matrix equation X equals zero. Um, we're obviously the right side is equal to zero. And the left side a here would just be, uh, a matrix of B one, b two, b three, and before combined. It's an augmented matrix. And X is a solution set which can only be 0000 if, um, the entire set of you one through before is linearly independent. Because since therefore, column backers, we're gonna solve it before variables causing this have four entries. So if you multiply these two together ah, and some chemicals zero, we would get zero of you won plus zero v two plus zero B three plus zero before equals zero. So even though this, um, problem tells us that consider this hint where this form of the equation where where you consider it zero to be the weight of before the only possible Bates for our waits for B one B two b three are zeros. Because the set is already linearly independent, any other value for these 1st 3 waits would contradict the statement, and it would be false, as the entire set together is already video. The only independent so different parts of the set, uh, better taken from the original set in this case, if you want me to be three, should also be literally

View More Answers From This Book

Find Another Textbook

Numerade Educator

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

Each statement in Exercises 33–38 is either true (in all cases) or false (fo…

For the following exercises, determine whether the statement is true or fals…

In Exercises 29 and $30, V$ is a nonzero finite-dimensional vector space, an…

Mark each statement True or False. Justify each answer on the basis of a car…

In Exercises 148–155, determine whether each statement is true or false. If …

01:52

In Exercises $33-36,$ verify that det $E A=(\operatorname{det} E)(\operatorn…

02:44

Let $T : \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}$ be a linear transformati…

01:08

In Exercises $7-14$ , cither use an appropriate theorem to show that the giv…

06:00

Let $A=L U$ be an LU factorization. Explain why $A$ can be row reduced to $U…

02:22

describe the possible echelon forms of the matrix. Use the notation of Examp…

03:35

Let $W$ be the union of the first and third quadrants in the $x y-$ plane. T…

In Exercises 19 and $20,$ find the parametric equation of the line through a…

01:37

Suppose that all the entries in $A$ are integers and det $A=1 .$ Explain why…

03:20

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.