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

Unless otherwise specified, assume that all matrices in these exercises are $n \times n .$ Determine which of the matrices in Exercises $1-10$ are invertible. Use as few calculations as possible. Justify your answers.$$[\mathbf{M}]\left[\begin{array}{rrrr}{4} & {0} & {-7} & {-7} \\ {-6} & {1} & {11} & {9} \\ {7} & {-5} & {10} & {19} \\ {-1} & {2} & {3} & {-1}\end{array}\right]$$

The $4 \times 4$ Matrix is invertible because it has four pivot positions by inverse matrix transform rule

Algebra

Chapter 2

Matrix Algebra

Section 3

Characterizations of Invertible Matrices

Introduction to Matrices

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:59

Unless otherwise specified…

02:16

02:32

04:12

03:33

01:15

02:02

00:53

00:58

02:18

For the following exercise…

for this exercise were considering a four by four matrix say that's displayed here, and our goal is to determine whether or not this matrix will be in vertebral by inspection. There doesn't seem to be anything interesting going on. I can't tell if the columns are linearly dependent, for example. And if we were to roll, reduce this matrix by hand, it would be a long and difficult journey, since these are not very friendly numbers. So for this particular exercise, it's encourage that we either use a computer algebra system or a calculator. I took the approach of using occurred a computer algebra system, and I found that this matrix ISRO equivalent to the following matrix here this is the four by four identity matrix, and from the statement that the Matrix A is roll equivalent to an identity matrix, it follows immediately that a is in vertebral. If, for example, though we did not have an entry one here, suppose it came out as a zero. We would have say that a is not in vertebral in that case, but for our situation. We do have a pivot in every row, so we have a number convertible matrix

View More Answers From This Book

Find Another Textbook

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

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

For the following exercises, use the matrices below to perform matrix multip…

03:26

Column vectors are written as rows, such as $\mathbf{x}=\left(x_{1}, x_{2}\r…

05:41

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

11:34

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

01:55

$[\mathbf{M}]$ Let $D=\left[\begin{array}{cccc}{.0040} & {.0030} & {…

03:13

In Exercises 11 and $12,$ give integers $p$ and $q$ such that Nul $A$ is a s…

01:38

If $A$ is an $n \times n$ matrix and the transformation $\mathbf{x} \mapsto …

03:00

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

03:19

Let $A$ be a $3 \times 4$ matrix, let $\mathbf{y}_{1}$ and $\mathbf{y}_{2}$ …

02:46

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

09:54

Exercises 1–4 refer to an economy that is divided into three sectors—manufac…

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.