### 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**

(choose chapter or problem)

**Get Unlimited Answers! Check out our subscriptions**

**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 \(2 x_{1}-x_{2}=0\).

###
Not The Solution You Need? Search for *Your* Answer Here:

### 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 \(2 x_{1}-x_{2}=0\).

**ANSWER:**

Step 1 of 7

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

### Reviews

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

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

No thanks, I don't want to help other students

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

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

No thanks, I don't want to help other students