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 \(\xvec = B\twovec{3}{-2}\text{.}\)

in-context