### Area of a Parallelogram Under a Linear TransformationLet $ S $ be the parallelogram determined by the vectors $ \mathbf{b}_1 = \begin{bmatrix} 7 \\ -5 \end{bmatrix} $ and $ \mathbf{b}_2 = \begin{bmatrix} 0 \\ 1 \end{bmatrix} $ and let $ A = \begin{bmatrix} 3 & 4 \\ 1 & 1 \end{bmatrix} $. Compute the area of the image of $ S $ under the mapping $ x \to Ax $.The area of the image of $ S $ under the mapping $ x \to Ax $ is \[ \boxed{\phantom{00}} \] (Type an integer or a decimal.)

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7 and bɔ 3 4 Let S be the parallelogram determined by the vectors b, and let A= Compute the area of the image of S under the mapping xAx. 11 The area of the image of S under the mapping XHAX is (Type an integer or a decimal)

7 and bɔ 3 4 Let S be the parallelogram determined by the vectors b, and let A= Compute the area of the image of S under the mapping xAx. 11 The area of the image of S under the mapping XHAX is (Type an integer or a decimal)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

### Area of a Parallelogram Under a Linear Transformation

Let $ S $ be the parallelogram determined by the vectors $ \mathbf{b}_1 = \begin{bmatrix} 7 \\ -5 \end{bmatrix} $ and $ \mathbf{b}_2 = \begin{bmatrix} 0 \\ 1 \end{bmatrix} $ and let $ A = \begin{bmatrix} 3 & 4 \\ 1 & 1 \end{bmatrix} $. Compute the area of the image of $ S $ under the mapping $ x \to Ax $.

The area of the image of $ S $ under the mapping $ x \to Ax $ is \[ \boxed{\phantom{00}} \] (Type an integer or a decimal.)

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