💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Stuck on your homework problem? This step-by-step video should help.

Try Numerade Free for 30 Days

Like

Report

In Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.$$\left[\begin{array}{rrr}{1} & {2} & {4} \\ {0} & {-3} & {1} \\ {0} & {0} & {-2}\end{array}\right]$$

$A^{-1}=\frac{1}{6}\left[\begin{array}{ccc}{6} & {4} & {14} \\ {0} & {-2} & {-1} \\ {0} & {0} & {-3}\end{array}\right]$

Algebra

Chapter 3

Determinants

Section 3

Cramer’s Rule, Volume, and Linear Transformations

Introduction to Matrices

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:58

In Exercises 11–16, comput…

04:57

07:40

06:02

07:19

01:57

For the following exercise…

00:46

Find the inverse of each m…

05:24

Find the inverse of each $…

02:54

11:00

in this video, we're gonna be solving problem number 16 from section 3.3, which is based on Kramer's Warren determinants. So here were given this initial, uh, matrix A, and we're told to find the inverse of a using their. The equation given interior meet with Basic says that the inverse of a matrix A is just one over. It's a determinant, times the adjective of a And here the idea of a is listed because the computation of the Advocate is a long and tedious and will not be shown in this video because it would make the video too long. So to find the adjective A all you have to do is find the co factor matrix of A and transpose it. So to find a co factor of one element in a So let's pick the 1st 1 you block out the row and call them. That is, um, that contains that element and take the two by two resulting determined of whatever's left, which is one singular co packer. And you repeat, repeat that with every term in a and you basically transpose it, which will give you this matrix. Uh, next up is to find the determinant of A, which is one times native, three times negative, two minus one time, zero minus two times zero times negative. Too minus one time. Zero plus four times These are times or ah, minus morning news three times zero. Which gives us, um, meticulous six. So a inverse is just 1/6 time's the address. So you just seal every element in the Advocate by 1/6. So you should get and rose to be one to third. Uh, 7/3 zero negative. 1/3. I got a born six zeros there on negative one. Now you get one, which is the inverse of the initial.

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 …

In Exercises 11–16, compute the adjugate of the given matrix, and then use T…

For the following exercises, find the multiplicative inverse of each matrix,…

Find the inverse of each matrix, if it exists.$$\left[\begin{array}{…

Find the inverse of each $2 \times 2$ matrix using matrix multiplication, eq…

Find the inverse of each matrix $A$ if possible. Check that $A A^{-1}=I$ and…

For the following exercises, find the inverse of the given matrix.

$…

03:22

If a mass $m$ is placed at the end of a spring, and if the mass is pulled do…

02:52

Determine which sets in Exercises $1-8$ are bases for $\mathbb{R}^{3}$ . Of …

01:24

Determine which sets in Exercises $15-20$ are bases for $\mathbb{R}^{2}$ or …

01:28

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

00:36

02:01

For each subspace in Exercises 1–8, (a) find a basis, and (b) state the dime…

03:28

Combine the methods of row reduction and cofactor expansion to compute the d…

03:47

Let $\mathbf{v}_{1}=\left[\begin{array}{r}{4} \\ {-3} \\ {7}\end{array}\righ…

Show that the space $C(\mathbb{R})$ of all continuous functions defined on t…

06:07

In Exercises 7–10, determine the values of the parameter s for which the sys…

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.