###### Preview Activity3.1.1
1. Explain how you would solve the equation $$3x = 5$$ without using the concept of division.

2. Find the $$2\times2$$ matrix $$A$$ that rotates vectors counterclockwise by $$90^\circ\text{.}$$

3. Find the $$2\times2$$ matrix $$B$$ that rotates vectors clockwise by $$90^\circ\text{.}$$

4. What do you expect the product $$BA$$ to be? Explain the reasoning behind your expectation and then compute $$BA$$ to verify it.

5. Solve the equation $$A\xvec = \twovec{3}{-2}$$ using Gaussian elimination.

6. Explain why your solution may also be found by computing $$\xvec = B\twovec{3}{-2}\text{.}$$

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