###### Preview Activity 3.1.1

Explain how you would solve the equation \(3x = 5\) without using the concept of division.

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

Find the \(2\times2\) matrix \(B\) that rotates vectors

*clockwise*by \(90^\circ\text{.}\)What do you expect the product \(BA\) to be? Explain the reasoning behind your expectation and then compute \(BA\) to verify it.

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

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