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Suppose that all the entries in $A$ are integers and det $A=1 .$ Explain why all the entries in $A^{-1}$ are integers.$$(0,-2),(5,-2),(-3,1),(2,1)$$

15

Algebra

Chapter 3

Determinants

Section 3

Cramer’s Rule, Volume, and Linear Transformations

Introduction to Matrices

Missouri State University

McMaster University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:29

Suppose that all the entri…

02:21

03:55

01:37

01:45

CHALLENGE If $a_{1}$ and $…

00:27

Explain why the whole numb…

01:57

If $A=\left[\begin{array}{…

01:49

Show that if $a | b$ and $…

08:26

Show that if $a$ and $b$ a…

01:16

If$$A=\left[\begin…

in this video, we're gonna be solving problem number 22 from the book from section through going through which the baseline determinants in the cream result and the area of parallel grounds. Um, so you were given four coordinates its label them a bcd and rasa. Find the area the parallelogram generated by these four coordinates. First, we need to find two factors that are part of that parallelogram. So we can do so by just, um So to find the vector a B, for example, we just take be just five negative, too. And subtract the accident like component from a car. Um, subtracting X and Y component of beef by a So you get the vector to be five minus zero, which is five common. I give to minus negative, too, which is negative. Two plus 20 So that's the first specter. And we need one more vector here. Ah, which is different from the first specter. So or perpendicular to so, um, way use the same one of the points has to be the same. So we use a as a common point. Um, so a C would be just the recover one minus zero common negative too, which is native three comma, one minus negative. Two is one plus two with three. So those are the two points We just put them in a, um in a two by two matrix. So five zero negative 33 And the area is that's called us A. So the area is the determinant of of this matrix a year on and take the absolute value of it. So it's gonna be five times three minus negative three times zero, which is absolutely of 15 because made of three times zero is just zero, possibly 15 is 15.

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