💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

For each subspace in Exercises 1–8, (a) find a basis, and (b) state the dimension.$$\{(a, b, c) : a-3 b+c=0, b-2 c=0,2 b-c=0\}$$

a. the subspace S has no basis.b. 0

Calculus 3

Chapter 4

Vector Spaces

Section 5

The Dimension of a Vector Space

Vectors

Johns Hopkins University

Missouri State University

Harvey Mudd College

Boston College

Lectures

02:56

In mathematics, a vector (…

06:36

02:28

For each subspace in Exerc…

05:10

06:03

02:01

01:25

02:55

For the matrices in Exerci…

01:53

06:08

In Exercises 11 and $12,$ …

03:25

Exercises $9-12$ display a…

10:03

(a) find $n$ such that row…

we'll get something. This problem were given subspace. That is a B C D. Where? A minus three B. Let's see. Zero. So by this equation, we know that see can be represented as freebie minus a So that means C can be determined by being a so our vector a B c D can be re read. Could be right. We can rewrite this vector. Um, terms off, eh? Hey, freebie mind, say, and the so. I noticed that A, B and D R V variables here. Well, c can be represented as, uh, A and B. So keep going. We can separate the specter so that it will be 10 91. I'm a skater. Eight and zero. 13 zero. Time Specter beak. And for the vector d off. Sorry. Should be scaler instead of Victor. Um, times of skated be And poor skater d we have There was 00 times skater d All right, so our pieces will be these three vectors. 10 negative. 10 013 and 0001 All right, So this is our faces and our dimension of this subspace. Well, the three

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…

For each subspace in Exercises 1–8, (a) find a basis, and (b) state the dime…

For the matrices in Exercises $17-20,(a)$ find $k$ such that Nul $A$ is a su…

In Exercises 11 and $12,$ find the dimension of the subspace spanned by the …

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

(a) find $n$ such that rowspace $(A)$ is a subspace of $\mathbb{R}^{n}$, and…

01:23

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

03:35

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

06:18

Determine if $P=\left[\begin{array}{cc}{.2} & {1} \\ {.8} & {0}\end{…

00:29

Is $\left[\begin{array}{r}{1} \\ {-2} \\ {1}\end{array}\right]$ an eigenvect…

03:02

Use Cramer’s rule to compute the solutions of the systems in Exercises 1–6.<…

02:46

Let $A$ be an $m \times n$ matrix and let $\mathbf{u}$ be a vector in $\math…

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

01:37

Let $A=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\righ…

04:20

In Exercises $7-12$ , assume the signals listed are solutions of the given d…

02:39

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

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.