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

Get the answer to your homework problem.

Like

Report

Exercises $27-29$ concern an $m \times n$ matrix $A$ and what are often called the fundamental subspaces determined by $A .$Use Exercise 28 to explain why the equation $A \mathbf{x}=\mathbf{b}$ has a solution for all $\mathbf{b}$ in $\mathbb{R}^{m}$ if and only if the equation $A^{T} \mathbf{x}=\mathbf{0}$ has only the trivial solution.

Therefore the equation $A x=b$ has a solution for all $b$ in $R^{m}$ .

Calculus 3

Chapter 4

Vector Spaces

Section 6

Rank

Vectors

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

02:56

In mathematics, a vector (…

06:36

04:00

Exercises $27-29$ concern …

02:27

06:26

Exercises $22-26$ provide …

15:15

02:29

Suppose $A$ is an $m \time…

06:33

Suppose $A$ is an $n \time…

05:13

03:25

Exercises $9-12$ display a…

07:04

Exercises $23-26$ display …

01:42

For the matrices in Exerci…

for set off. The question is, is you could do be who have so listen or oh, bad dreams or B in our, um Yeah, the diamond Sinar column Space off. He must be goto m know when this is true. In the previous question, we have calculator. We have that here on their times, you know, Hold on space off air paths, diamonds and up No space off a transpose is equal m no sense. This is m Therefore, this must be zero. So this is true. I'm leaving the diamonds and off another face off you Transport is a zero on this is zero The solution metrics. Uh, a transpose is trivial. That is mhm when another hour diamonds and honor off your transfer zero Then you get to do the here Transfers into X has trivial Feddersen. So therefore yeah, this is possible only and only when a transpose x trivial solution Mhm

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…

Exercises $27-29$ concern an $m \times n$ matrix $A$ and what are often call…

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

Suppose $A$ is an $m \times n$ matrix with the property that for all $\mathb…

Suppose $A$ is an $n \times n$ matrix with the property that the equation $A…

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…

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

02:00

In Exercises $7-12$ , use Example 6 to list the eigenvalues of $A$ . In each…

04:42

In Exercises 17 and 18 , $A$ is an $m \times n$ matrix. Mark each statement …

00:42

Construct a nondiagonal $2 \times 2$ matrix that is diagonalizable but not i…

03:15

Rank 1 matrices are important in some computer algorithms and several theore…

01:54

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

03:21

Let $\left\{y_{k}\right\}$ be the sequence produced by sampling the continuo…

01:12

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

01:47

01:53

In Exercises $13-20,$ find an invertible matrix $P$ and a matrix $C$ of the …

03:17

[M] Show that $\left\{1, \cos t, \cos ^{2} t, \ldots, \cos ^{6} t\right\}$ i…

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.