### Solution Found! # Give 2 2 matrices A so that for any x R2 we have, respectively: a. Ax is the vector

Chapter 2, Problem 5

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QUESTION:

Give $$2 \times 2$$ matrices A so that for any $$\mathbf{x} \in \mathbb{R}^{2}$$ we have, respectively:

a. Ax is the vector whose components are, respectively, the sum and difference of the components of x.

b. Ax is the vector obtained by projecting x onto the line $$x_{1}=x_{2} \text { in } \mathbb{R}^{2}$$.

c. Ax is the vector obtained by first reflecting x across the line $$x_{1}=0$$ and then reflecting the resulting vector across the line $$x_{2}=x_{1}$$.

d. Ax is the vector obtained by projecting x onto the line $$2 x_{1}-x_{2}=0$$.

e. Ax is the vector obtained by first projecting x onto the line $$2 x_{1}-x_{2}=0$$ and then rotating the resulting vector $$\pi / 2$$ counterclockwise.

f. Ax is the vector obtained by first rotating x an angle of $$\pi / 2$$ counterclockwise and then projecting the resulting vector onto the line $$2 x_{1}-x_{2}=0$$.

### Questions & Answers (2 Reviews)

QUESTION:

Give $$2 \times 2$$ matrices A so that for any $$\mathbf{x} \in \mathbb{R}^{2}$$ we have, respectively:

a. Ax is the vector whose components are, respectively, the sum and difference of the components of x.

b. Ax is the vector obtained by projecting x onto the line $$x_{1}=x_{2} \text { in } \mathbb{R}^{2}$$.

c. Ax is the vector obtained by first reflecting x across the line $$x_{1}=0$$ and then reflecting the resulting vector across the line $$x_{2}=x_{1}$$.

d. Ax is the vector obtained by projecting x onto the line $$2 x_{1}-x_{2}=0$$.

e. Ax is the vector obtained by first projecting x onto the line $$2 x_{1}-x_{2}=0$$ and then rotating the resulting vector $$\pi / 2$$ counterclockwise.

f. Ax is the vector obtained by first rotating x an angle of $$\pi / 2$$ counterclockwise and then projecting the resulting vector onto the line $$2 x_{1}-x_{2}=0$$.

Step 1 of 7

A is a 2x2 matrix and $$x \in {R^2}$$.

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### Review this written solution for 964540) viewed: 334 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 2.2 - Problem 5

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Textbook: Linear Algebra: A Geometric Approach

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