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

Show that $I_{m} A=A$ when $A$ is an $m \times n$ matrix. You can assume $I_{m} \mathbf{x}=\mathbf{x}$ for all $\mathbf{x}$ in $\mathbb{R}^{m} .$

$I_{m} A=A$

Algebra

Chapter 2

Matrix Algebra

Section 1

Matrix Operations

Introduction to Matrices

Campbell University

Oregon State University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

03:03

Show that $A I_{n}=A$ when…

08:16

Let $A$ be an $m \times n$…

02:13

05:50

Identity Matrix Let $A=\le…

04:14

Let $\mathbf{A}$ be an $n …

04:04

Prove that if $A$ is an $m…

05:04

Let $A=\left[a_{i j}(t)\ri…

03:00

06:28

02:31

Let $A$ be an $n \times n$…

in this video, we're considering a matrix A and what we have is that a is written down in this notation. Here were a one through a n or the columns of a There's an columns. Africanus Assume that each column has m entries. So that overall Hamza M by N matrix. Now what we're going to do next is consider this matrix, which is I am. This is going to be a square matrix of M rose and in columns, which is also the identity matrix. That means we can write it in column form using the same kind of notation with the one you too up through E I m. As this way. So this is our identity matrix and recall if we pick any one of these columns, E one just means we have a matrix for excuse me, a vector with M entries and one will be in entry one for this 11 is going to be in the last entry em one will be in the second entry of this vector and so on. So what we're going to be do doing next is multiplying the identity matrix. I am with our metrics, a Let's write out what this would look like using our rule for matrix multiplication. You would take the entire matrix I I M and multiply by the first column of a, which is a one. Then the second calm of the product is going to be. I am times the second calm of a, which is a step, too. Then lastly, we go off to the last column of the product I am times A. And that would be the identity matrix times the last column of a a sub in. So this is what the product would look like so far, but also recalled that the identity matrix multiplying any vector always gives us back that same vector. So in our case, when we look at these products here, this is really just overall in a one. Let's write that out in our next step. So we have died. Any matrix times A is now equal to a one A to through a sub en. Since thes identity matrices do not change the Matrix Times, the vector product, it just gives us back those vectors. But now that we get to this stage, recall that this is the definition of the Matrix A. So we have just shown that we take an M by N i DNT matrix multiplied by a raise of size M Then we get back just that matrix A itself.

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 …

Show that $A I_{n}=A$ when $A$ is an $m \times n$ matrix. [Hint: Use the (co…

Let $A$ be an $m \times n$ matrix with colspace $(A)=$ nullspace(A). Prove t…

Let $A$ be an $m \times n$ matrix and let 0 be the $m \times n$ matrix that …

Identity Matrix Let $A=\left[a_{i j}\right]$ be an $n \times n$ matrix. Prov…

Let $\mathbf{A}$ be an $n \times n$ zero-one matrix. Let $\mathbf{I}$ be the…

Prove that if $A$ is an $m \times n$ matrix and $D=$ $\operatorname{diag}\le…

Let $A=\left[a_{i j}(t)\right]$ be an $m \times n$ matrix function and let $…

Let $A$ be an $m \times n$ matrix and let $B$ be an $p \times n$ matrix. Use…

Let $A$ be an $m \times n$ matrix. Show that the columns of $A$ are linearly…

Let $A$ be an $n \times n$ matrix with $A^{4}=0 .$ Prove that $I_{n}-A$ is i…

02:41

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

Find another set of equilibrium prices for the economy in Example $1 .$ Supp…

02:01

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

02:36

Let $T : \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ be the transformation th…

01:40

Exercises $1-4$ display sets in $\mathbb{R}^{2}$ . Assume the sets include t…

02:34

Show that the transformation in Exercise 8 is merely a rotation about the or…

04:52

Let $A=\left[\begin{array}{rr}{2} & {5} \\ {-3} & {1}\end{array}\rig…

02:37

Find the value(s) of $h$ for which the vectors are linearly dependent. Justi…

03:32

$$\mathbf{u}=\left[\begin{array}{l}{0} \\ {4} \\ {4}\end{array}\right] \…

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.