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 in $\mathbb{R}^{4}$ and $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}$ is linearly dependent, then $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}, \mathbf{v}_{4}\right\}$ is also linearly dependent.

True

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 7

Linear Independence

Introduction to Matrices

Missouri State University

Campbell University

Oregon State University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

02:36

Each statement in Exercise…

02:00

02:24

02:42

02:13

06:33

In Exercises 29 and $30, V…

03:54

Mark each statement True o…

02:07

In Exercises 21 and 22, ma…

01:01

Decide whether each statem…

05:34

In Exercises 77–80, determ…

In this example, we have a set of four different vectors, each coming from the space are for Let's make a specific assumption about this set of vectors. Let's assume that the set v one, v two, v three. So just the 1st 3 vectors is a linearly dependant set of vectors. Let's see what this would mean specifically if, for example, we let a be a matrix formed from the columns V one V to V three, which we said already is linearly dependent as well as before. So this introduces a little bit of extra drama in this linear algebra problem. If these vectors are linearly dependent and we threw in 1/4 1 can we save this and make the set linearly independent? Well, to determine that, let's first consider the Matrix equation eight times X equals zero vector. Well, we know that V one v two V three is linearly dependent hoops thought that was the high. Later there we go. And since b one b two B three is linearly dependent, it follows that this equation has nontrivial solutions by the definition of linear dependence. But let's say what that would mean, since there are nontrivial solutions that would imply that A does not have a pivot in every column where the word every is probably the most important word here, since A does not have a pivot in every column that next implies immediately by the definition of linear dependence that the columns of A are linearly dependent. So just because we knew that these are dependent, throwing in 1/4 vector does not change the dependence of the set. If we start with a linearly dependent set, extending the set still is going to be linearly dependent, it's our conclusion is that the set of vectors V one, the two V three and before is linearly dependent. The set of vectors could have been really something like 100 vectors of anything we wanted. But as soon as we know that the 1st 3 a linearly dependent, the rest are linearly dependent as well

View More Answers From This Book

Find Another Textbook

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…

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 21 and 22, mark each statement True or False. Justify each answ…

Decide whether each statement is true or false, and explain why.

If …

In Exercises 77–80, determine whether each statement is true or false. If th…

01:31

Compute det $B^{4},$ where $B=\left[\begin{array}{lll}{1} & {0} & {1…

05:41

Exercises $22-26$ provide a glimpse of some widely used matrix factorization…

08:45

IM Suppose an experiment leads to the following system of equations:$4.5…

01:37

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

13:52

Design two different ladder networks that each output 9 volts and 4 amps whe…

01:33

Find the determinants in Exercises $15-20,$ where$$\left|\begin{arra…

01:35

In Exercises 21 and $22,$ find a parametric equation of the line $M$ through…

04:43

Find an LU factorization of the matrices in Exercises $7-16$ (with $L$ unit …

In Exercises 17 and $18,$ mark each statement True or False. Justify each an…

00:33

Compute the determinants of the elementary matrices given in Exercises $25-3…

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.