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

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

Try Numerade Free for 30 Days

Like

Report

Describe the possible echelon forms of the matrix. Use the notation of Example 1 in Section 1.2.$A$ is a $4 \times 2$ matrix, $A=\left[\begin{array}{ll}{a_{1}} & {a_{2}}\end{array}\right],$ and $a_{2}$ is not a multiple of $a_{1} .$

$\left[ \begin{array} { l l } { \mathbf { i } } & { * } \\ { 0 } & { \mathbf { i } } \\ { 0 } & { 0 } \\ { 0 } & { 0 } \end{array} \right] \cdot \left[ \begin{array} { l l } { 0 } & { \mathbf { i } } \\ { 0 } & { 0 } \\ { 0 } & { 0 } \\ { 0 } & { 0 } \end{array} \right]$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 7

Linear Independence

Introduction to Matrices

McMaster University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:29

describe the possible eche…

03:03

Describe the possible eche…

00:32

02:55

Find a row echelon form fo…

02:38

Write the matrix in row-ec…

02:54

02:31

01:00

03:16

01:51

in this example were considering a matrix A which is going to be of size four by two, meaning it how it will have two columns, each with four entries, and will use this notation to describe the matrix. A first suppose further that a one and a two are not multiples of each other. What this would mean because we're considering just two vectors is that the set a one a to is linearly independent. If they were multiples of each other, we would have said that this set a one. A two must then be linearly dependent. In that case. Well, now that we know that the columns of the Matrix A are linearly independent, we could write what the form of a would be using just generic elements. We would have a would be about this size with four rows, two columns, and I'll put a solid box here in the first entry. This means this is any real number that's not zero star says. This could be any real number whatsoever. Ah, places zero here and another solid box. Well, rectangle in this case, then zeros down below. So knowing that a one a two are not multiples of each other, tells us that there are no free variables, which tells us we will have a pivot in both columns. So this is what the row reduce echelon form of a would look like. Now let's change us a little bit. Let's say suppose a tu is not a multiple of a one. This statement feels like it's almost exactly the same as this statement that a one and a two are not multiples of each other. But it turns out there is a difference. If a two is not a multiple of a one, there is a possibility that a one could be the zero vector. That means in this case, the generic format for a could potentially look like this 00 and zero for the first Vector 81 and we could have a generic but non zero entry here for a two. We're putting an entry here. That's not zero, because if a two was the zero vector, then it would be a multiple of a one for any real number. So the generic form of The Matrix say takes on this shape. So there's really two different cases. A could either be this or this

View More Answers From This Book

Find Another Textbook

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

describe the possible echelon forms of the matrix. Use the notation of Examp…

Describe the possible echelon forms of the matrix. Use the notation of Examp…

Find a row echelon form for the matrix.$$\left[\begin{array}{rrr}{1} &am…

Write the matrix in row-echelon form. Remember that the row-echelon form of …

Find a row echelon form for the matrix.$$\left[\begin{array}{rrrr}{1} &a…

06:43

In Exercises 23 and $24,$ mark each statement True or False. Justify each an…

The expansion of a $3 \times 3$ determinant can be remembered by the followi…

01:52

In Exercises $33-36,$ verify that det $E A=(\operatorname{det} E)(\operatorn…

02:14

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

05:06

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

02:01

Determine by inspection whether the vectors are linearly independent. Justif…

06:57

Mark each statement True or False. Justify each answer.a. If $\mathbf{f}…

00:29

Compute the determinants of the elementary matrices given in Exercises $25-3…

01:37

Suppose that all the entries in $A$ are integers and det $A=1 .$ Explain why…

Find formulas for X, Y, and Z in terms of A, B, and C, and justify your calc…

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.