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

In Exercises 11 and $12,$ find the dimension of the subspace spanned by the given vectors.$$\left[\begin{array}{r}{1} \\ {-2} \\ {0}\end{array}\right],\left[\begin{array}{r}{-3} \\ {4} \\ {1}\end{array}\right],\left[\begin{array}{r}{-8} \\ {6} \\ {5}\end{array}\right],\left[\begin{array}{r}{-3} \\ {0} \\ {7}\end{array}\right]$$

3

Calculus 3

Chapter 4

Vector Spaces

Section 5

The Dimension of a Vector Space

Vectors

Missouri State University

Campbell University

Idaho State University

Boston College

Lectures

02:56

In mathematics, a vector (…

06:36

03:48

In Exercises 13 and 14, fi…

03:43

In Exercises $7-10,$ let $…

04:56

01:51

In Exercises $15-18,$ find…

03:06

Let $\mathbf{v}_{1}=\left[…

03:10

02:13

03:25

Exercises $9-12$ display a…

03:13

05:27

here we have the four Rector's. It's been such a subspace. That is, 12 zero. Think of 34 one and noted eight, six, five and negatives 30 seven. Excuse me. So, in order to check whether this is four vectors, are you nearly end end? One approach I would recommend is to apply the gushing illumination and check the reduce station warm to see Hi. If there is an theories and then travel and trivial solution. If there is, then that means the's four by four vectors are leaner depended. So we're done. So Okay, so to do the cash indignation. Oh, just right down First on the first page here and now we'll we'll keep going to the second page. Okay, so we first views. Second row, plus two, two times. The first road myself. The first rule. So that is fun. Next three, activate connective three, 23 And so the second rule will be zero. But first century and two Sorry. Connected to the second entry. And negative 10 with 1/3 entry, connective six. Or, uh, third entry for the fourth entry. And we'll keep the the last roll. Okay, Next, we will try to reduce the the last roll here. We usedto third row plus twice out the third row. Plus, um, that's the second rule. Okay, so first row were not changed. So that is one negative three reactivate a negative three. And so second rule was still being active to connective 10 and neck of six. Well, that's certainly the third row. We have zero first and cereal with 1/3 entry and two times 7 14 minus six iss eight. All right, so we don't need we don't even we don't even need to redo. Keep reducing, because right now we can We can know whether there are where there is a nontrivial solution. So we first have um x one minus three, x two plus eight Sorry, minus eight. Minus eight x three finest three x four minus three x for is zero. And we have negative too. Thanks to minus 10. Next three finest six x four. It's zero and eight times. Explore is always zero. So export zero. But we still have X y extracts three. Right. So first thing we have next one minus three x d'oh. Minus aid x three. It's zero and connected to x two minus 10 X tree. It's Darryl well, ex for zero so we can find from thes you questions that x two x three and, um, yaks. Three is a free, bearable, and X two can be determined by X three and X one can be determined by X two and x three. So that means there's there exists athletes and nontrivial solution. So that means these four vectors Do you want to three Before are we nearly dependent? Independent dependent. So that implies dimension off the subspace it's for.

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

In Exercises 13 and 14, find a basis for the subspace spanned by the given v…

In Exercises $7-10,$ let $W$ be the subspace spanned by the $\mathbf{u}^{\pr…

In Exercises $15-18,$ find a basis for the space spanned by the given vector…

Let $\mathbf{v}_{1}=\left[\begin{array}{r}{1} \\ {0} \\ {-1}\end{array}\righ…

Exercises $9-12$ display a matrix $A$ and an echelon form of $A$ . Find base…

02:26

Repeat Exercise 27 with $\mathbf{b}_{1}=\left[\begin{array}{r}{4} \\ {-7}\en…

00:33

Each equation in Exercises $1-4$ illustrates a property of determinants. Sta…

06:47

Use coordinate vectors to test whether the following sets of polynomials spa…

02:46

Find the volume of the parallelepiped with one vertex at the origin and adja…

01:07

Determine the dimensions of Nul $A$ and $\mathrm{Col} A$ for the matrices sh…

02:39

$[\mathbf{M}]$ Let $H=\operatorname{Span}\left\{\mathbf{v}_{1}, \mathbf{v}_{…

04:57

In Exercises 11–16, compute the adjugate of the given matrix, and then use T…

03:20

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

01:15

In Exercises $9-16,$ find a basis for the eigenspace corresponding to each l…

01:12

Use Exercise 27 to complete the proof of Theorem 1 for the case when $A$ is …

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.