💬 👋 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

Suppose that all the entries in $A$ are integers and det $A=1 .$ Explain why all the entries in $A^{-1}$ are integers.$$(0,0),(-2,4),(4,-5),(2,-1)$$

6

Algebra

Chapter 3

Determinants

Section 3

Cramer’s Rule, Volume, and Linear Transformations

Introduction to Matrices

Missouri State University

Oregon State University

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

02:08

Suppose that all the entri…

01:37

02:29

03:55

00:27

Explain why the whole numb…

01:45

CHALLENGE If $a_{1}$ and $…

00:45

In Exercises $1-4$a. G…

Let $A=\left[\begin{array}…

04:38

Prove that each statement …

01:49

Show that if $a | b$ and $…

in this video, we're gonna be selling problem number 20 from section 3.3 of the book, which is based on determinants and ah Cramer's rule. So, um, it gives us four points or or coordinates and then it the question asked us to find the area the parallelogram generated by these coordinates to do so, we just need to find two vectors of that parallelogram and take their determinant. So it's easiest to label these first a B, c d. And we need to find two vectors. And since a a 00 let's make it easier to start with 00 So the vector a B would be, um, the coordinate B minus A. It just gives us ah, negative to come up for because negative to minus zero is negative. And for many zeroes Ah, for And the vector um, the vector a c would be ah, for native five because it's again subtraction by zero is the same. Um, and we put these in in a parallelogram are in a two by two determinant like this because they're vectors are two sides of a matrix are not a matrix. A parallelogram on the on the coordinate plan, and And we take the cross product here, which is, um, negative. Negative. Two times negative. Five minus four times four times four. Yeah, which is just, uh, 10 minus 16. And you take the absolute value. The determinant to find, um, the area so area pickles, absolutely. Of the chairman of A, which is call the absolute value of 10 minus six years, which is equal to six.

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 …

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

Explain why the whole numbers are a subset of the integers.

CHALLENGE If $a_{1}$ and $r$ are integers, explain why the value of $\frac{a…

In Exercises $1-4$a. Give the order of each matrix.b. If $A=\left[a_…

Let $A=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\righ…

Prove that each statement is true for all positive integers. $$\frac…

Show that if $a | b$ and $b | a,$ where $a$ and $b$ are integers, then $a=b$…

02:03

Use Exercises $25-28$ to answer the questions in Exercises 31 and $32 .$ Giv…

00:53

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

01:53

For the matrices in Exercises $17-20,(a)$ find $k$ such that Nul $A$ is a su…

02:09

In Exercises 15 and $16,$ mark each statement True or False. Justify each an…

03:27

Let $H$ be an $n$ -dimensional subspace of an $n$ -dimensional vector space …

02:26

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

03:01

Find the determinants in Exercises 5–10 by row reduction to echelon form.

02:00

Find the dimension of the subspace of all vectors in $\mathbb{R}^{3}$ whose …

In Exercises $5-8,$ find the coordinate vector $[\mathbf{x}]_{\mathcal{B}}$ …

01:57

Find bases for the null spaces of the matrices given in Exercises 9 and $10 …

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.