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# Given x = (2, 3) and y = (1, 1), calculate the following algebraically and sketch a

**Chapter 1, Problem 1**

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**QUESTION:**

1. Given x = (2, 3) and \(y=(-1,1)\), calculate the following algebraically and sketch a picture to show the geometric interpretation.

a. x + y

b. \(\mathbf{x}-\mathbf{y}\)

c. x + 2y

d. \(\frac{1}{2} \mathbf{x}+\frac{1}{2} \mathbf{y}\)

e. \(y-x\)

f. \(2 \mathbf{x}-\mathbf{y}\)

g. \(\|\mathbf{x}\|\)

h. \(\frac{\mathbf{x}}{\|\mathbf{x}\|}\)

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### Questions & Answers

**QUESTION:**

1. Given x = (2, 3) and \(y=(-1,1)\), calculate the following algebraically and sketch a picture to show the geometric interpretation.

a. x + y

b. \(\mathbf{x}-\mathbf{y}\)

c. x + 2y

d. \(\frac{1}{2} \mathbf{x}+\frac{1}{2} \mathbf{y}\)

e. \(y-x\)

f. \(2 \mathbf{x}-\mathbf{y}\)

g. \(\|\mathbf{x}\|\)

h. \(\frac{\mathbf{x}}{\|\mathbf{x}\|}\)

**ANSWER:**

Step 1 of 9