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Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at $(1,3,0),(-2,0,2),$ and $(-1,3,-1)$

18

Algebra

Chapter 3

Determinants

Section 3

Cramer’s Rule, Volume, and Linear Transformations

Introduction to Matrices

McMaster University

Harvey Mudd College

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

02:49

Find the volume of the par…

01:00

01:16

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03:34

05:53

01:27

Find the indicated area or…

01:20

03:15

Find the volume of the giv…

09:00

Find the maximum volume of…

in this video, we're gonna be solving problem number 24 of section 3.3, which is based on, um, Cramer's rule in determinants, um, and volumes. So this question gives us for, um, for four coordinates in a three dimensional planes and, uh, your dimensional space and it asked says that find the bowling with the parallel a pit. So too, do Soviet. The first American victors thio from eight to each of these points because the first given point is the origin and you subtract be from a In this case, if you want to find a vector for a B which B minus 000 is just be so the vector is just gonna be be, um a c would be c needed to 02 and the a d we'll be d which is negative. 1 30 A negative one. Um, now we just set them in a three by three matrix and take the determinant. So find the in the area of the parallel activity. So the determinant of what's called us A would be and take its absolute value to find the area would be, um, one times zero times negative one Yeah, Minus two times through Linus. Three times. Make it two times and they have one minus two times plus zero times. Negative. Two times three minus zero times. Negative, boy. So this is just canceled because it's a zero time you're multiplying by zero. Um, and the rest of it will be one times negative. Six minus three times late of two times. They want us to minus negative to those four. So it would be negative. Six minus 12 which is negative. 18. And you take the absolute value Minute, which is 18 is the volume of the parallel of it.

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