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

Watch this step-by-step video, matched to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Exercises $9-12$ display a matrix $A$ and an echelon form of $A$ . Find bases for $\operatorname{Col} A$ and $\mathrm{Nul} A,$ and then state the dimensions of these subspaces.$$\begin{aligned} A &=\left[\begin{array}{rrrrr}{1} & {2} & {-5} & {0} & {-1} \\ {2} & {5} & {-8} & {4} & {3} \\ {-3} & {-9} & {9} & {-7} & {-2} \\ {3} & {10} & {-7} & {11} & {7}\end{array}\right] \\ & \sim\left[\begin{array}{ccccc}{1} & {2} & {-5} & {0} & {-1} \\ {0} & {1} & {2} & {4} & {5} \\ {0} & {0} & {0} & {1} & {2} \\ {0} & {0} & {0} & {0} & {0}\end{array}\right] \end{aligned}$$

32

Algebra

Chapter 2

Matrix Algebra

Section 9

Dimension and Rank

Introduction to Matrices

Missouri State University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

03:25

Exercises $9-12$ display a…

03:13

07:02

Exercises $23-26$ display …

07:04

08:16

Find an orthogonal basis f…

01:57

Find bases for the null sp…

06:08

In Exercises 11 and $12,$ …

16:00

08:41

In Exercises 1–4, assume t…

09:25

again in this question, You want to find the color space and no spice all this matrix right here. So to find the column space, all we need to do is to find a pivot follows off this matrix right here at this difficult. The pivot columns are the same pivot columns as those in its road echelon formed, right? Yeah. So we have about it. Havoc, homes being these three forms. So therefore, our column Ah, calmness face is simply columns face for a He's a span. All of these four metres. 154 minds too native four muted mine medicated wine five and finally 387 and six To find a null space off A you take its right echelon form and you want to Seoul. So if you said this is going to be you want to solve b X is it itches. So in parametric form, you want to solve 002000 minus 4100 three months. 20030 minus five is there and also rose. So then you wanna solve x one x two x three Export and x So you know in what this line tells you is x one plus two x two minus four extra plus three Export plus three x five is equal to zero. Just sold for X one you put minus two to decide. Plus fallin decide my street and my street. So this is going to be negative two x two plus by four x three minus three x four minus three x so x two There is no people calling for extra extra is just simply x two x three is going to be just simply two x four to export. Would you get from which he gets from this line right here. Now explore also had people call him. So export is just X for and X five we get from this one, which is negative X five music to zero x five is just is there So our mole space No space over a moment. Okay, Is the span off these actors? Minus 2000 And this is one, um full. 0000 Negative. 30 210 If and finally native 3000

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 …

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

Exercises $23-26$ display a matrix $A$ and an echelon form of $A .$ Find a b…

Find an orthogonal basis for the column space of each matrix in Exercises $9…

Find bases for the null spaces of the matrices given in Exercises 9 and $10 …

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

In Exercises 1–4, assume that the matrix A is row equivalent to B. Without c…

01:06

$[\mathbf{M}]$ Is it true that $\operatorname{det} A B=(\operatorname{det} A…

01:41

Compute the determinants in Exercises $1-8$ using a cofactor expansion acros…

06:26

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

02:53

Suppose a linear transformation $T : \mathbb{R}^{n} \rightarrow \mathbb{R}^{…

07:19

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

03:39

Show that if three shunt circuits (with resistances $R_{1}, R_{2}, R_{3} )$ …

00:39

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

03:11

Find the determinants in Exercises 5–10 by row reduction to echelon form.

08:29

Use partitioned matrices to prove by induction that for $n=2,3, \ldots,$ the…

03:48

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

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.