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Let $\mathbf{u}=\left[\begin{array}{l}{a} \\ {b}\end{array}\right]$ and $\mathbf{v}=\left[\begin{array}{l}{c} \\ {0}\end{array}\right],$ where $a, b,$ and $c$ are positive (for simplicity). Compute the area of the parallelogram determined by $\mathbf{u}, \mathbf{v}, \mathbf{u}+\mathbf{v},$ and $\mathbf{0},$ and compute the determinants of the matrices $[\mathbf{u} \quad \mathbf{v}]$ and $[\mathbf{v} \quad \mathbf{u}] .$ Draw a picture and explain what you find.

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Algebra

Chapter 3

Determinants

Section 1

Introduction to Determinants

Introduction to Matrices

Missouri State University

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

03:01

a. coordinate Geometry Fin…

Let $A$ and $B$ be $4 \tim…

02:49

Find the area of the paral…

02:12

02:30

Let $\mathcal{B}=\left\{\m…

01:29

02:38

00:50

02:51

okay, In this question, we want to basically find the relationship between areas on determinants. So drawing out vectors, you draw you. We have a zing to exit into a So that's why that a And why is it going to be put out there? So you is going to be like this on and be just simply existed to see why this is so V. Now I see adding the practice together, we just sent you a cool one break down to the other. So putting being onto you is just going to have that on this is longing to meet you custody. So the parallelogram that we're looking at is probably okay. Now, to find the area of this, we need to find the width and height off this pallet. So the wit just hear his length, See the height, his height he's gone through life, Be so the reason why does it say it's just simply because this spectre is length C and B is because the hype here is Be so the area off out of the program Oh, how the gram is equal to be a type of sin. Now you'll be taken to take that determines Oh, you be This is not to be the turn it off A B and C N zero. So this is equal to eight times zero. Given me zero minus few times C, which is easy. Its terminus on the year is equal to see zero a and B which is like to see Thomas being which gives you a B c. Why does a time zero which is your then what you see is that the area of the parallelogram is three time. See, while that if you take the absolute value off the determinants, you also get the sea. So the area off Powell other ground is equal to the absolute value off determinants. All you, Andy, we'll be in doesn't matter.

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