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YZ

# \begin{array}{l}{\text { a. Solve the system }} \\ {u=2 x-3 y, \quad v=-x+y} \\ {\text { for } x \text { and } y \text { in terms of } u \text { and } v . \text { Then find the value of the }} \\ {\text { Jacobian } \partial(x, y) / \partial(u, v)} \\ {\text { b. Find the image under the transformation } u=2 x-3 y \text { , }} \\ {v=-x+y \text { of the parallelogram } R \text { in the } x y \text { -plane with }} \\ {\text { boundaries } x=-3, x=0, y=x, \text { and } y=x+1 . \text { Sketch }} \\ {\text { the transformed region in the } u v \text { -plane. }}\end{array}

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##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

So first we have new Equus to two X minus three way and agree Eco's well, im on his ex. It's a soft exploit for you, B We're gonna have executes two connective. You plus three. And why? Because nectar you plus two b So the geico been is next. 12312 The answer is thinking one. And for the region we know that in the orders for playing, we have executed three with Transforms to you plus three weeks in for three x zero It's gonna goes to you plus three equals zero in the White House to ex transformed to vehicle Ciro. Why? Because Jax plus one chance for him to be equals one. So at the last, at last, we're gonna have a program. Oh, no. Where are you? You will be playing. So it's gonna basically look at this. Here is one. And, uh, next three. Whoa. Here's 30 This is 01 and this is 00 It's a little grand, Mr. Region

YZ
University of Illinois at Urbana-Champaign

#### Topics

Limits

Integrals

Multiple Integrals

##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp