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

Construct a $3 \times 3$ matrix, not in echelon form, whose columns span $\mathbb{R}^{3} .$ Show that the matrix you construct has the desired property.

since there are 3 pivot columns they span $\mathbb{R}^{3}$ .

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 4

The Matrix Equation Ax D b

Introduction to Matrices

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

01:39

Construct a $3 \times 3$ m…

03:53

If $A$ is an arbitrary $3 …

04:16

Suppose $A$ is a $3 \times…

02:40

06:41

Show that a $3 \times 7$ m…

01:25

Construct a nonzero $3 \ti…

01:22

Prove that a 3 by 3 determ…

02:46

01:20

Prove each of the followin…

02:02

In this example, we have a three by three matrix which has been constructed. This particular matrix is not initial inform, and that's strictly due to this negative six quantity, which is represented here, highlighted in yellow. Let's analyze this matrix further by putting it in echelon form. Once it's a natural inform, we will be able to analyze its pivots. So for my first row operation, we're going to eliminate this negative six. So let me copy Row One and grow to next multiply row two by three so that we can add it to Row three, the result of B zero zero and one. Now that the Matrix is in its echelon form, we have a pivot here that we can analyze here and here. In other words, this matrix. If we decide to call it a allows us toe show that A has a pivot in every row having a pivot and every row is now very special for this matrix. Because we have a pivot in every row, that's logically equivalent. It's all right to the bi directional implication, simple to the statement that the columns of a spans are three where the three comes from specifically the fact that we have three rows. So for this particular matrix, we have an example where there's a pivot in every row and therefore the columns of this matrix will spend its space are three.

View More Answers From This Book

Find Another Textbook

In mathematics, the absolute value or modulus |x| of a real number x is its …

Construct a $3 \times 3$ matrix, not in echelon form, whose columns do not s…

If $A$ is an arbitrary $3 \times 3$ matrix, use cofactor expansion to show t…

Suppose $A$ is a $3 \times n$ matrix whose columns span $\mathbb{R}^{3}$ . E…

Construct a $3 \times 3$ matrix $A,$ with nonzero entries, and a vector $\ma…

Show that a $3 \times 7$ matrix $A$ with nullity $(A)=4$ must have colspace …

Construct a nonzero $3 \times 3$ matrix $A$ and a vector $\mathbf{b}$ such t…

Prove that a 3 by 3 determinant in which the entries in column 1 equal those…

Suppose $A$ is a $3 \times 3$ matrix and $b$ is a vector in $\mathbb{R}^{3}$…

Prove each of the following statements for any $3 \times 3$ matrix $A$.I…

07:11

Given $A$ and $b$ in Exercises 11 and $12,$ write the augmented matrix for t…

02:35

In a certain region, about 7$\%$ of a city's population moves to the su…

01:26

Is it possible for a $5 \times 5$ matrix to be invertible when its columns d…

02:41

In a certain region, about 6% of a city’s population moves to the surroundin…

The given matrix determines a linear transformation $T .$ Find all $\mathbf{…

01:19

Unless otherwise specified, assume that all matrices in these exercises are …

03:22

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

08:35

Exercises 15 and 16 concern arbitrary matrices $A, B,$ and $C$ for which the…

03:23

In Exercises $7-12$ , describe all solutions of $A \mathbf{x}=0$ in parametr…

02:45

Write a matrix equation that determines the loop currents. [M] If MATLAB or …

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.