Least Squares: the Best Approximate Solution of Ax = B Worksheet with Answer Key

What's on the worksheet

1. Consider the system Ax = b with A = \begin{bmatrix} 1 & 1 \\ 2 & -1 \\ 1 & 2 \end{bmatrix}, \qquad \mathbf{b} = \begin{bmatrix} 4 \\ 6 \\ -7…
2. Mia brews a batch of kombucha and measures the sugar left in it, in grams per liter, on days t = 1, 2, 3, 4, 5 of fermenting:
3. A paddleboard rental on a lake counts the boards out on the water at t = 0, 1, 2, 3, 4 hours after it opens:
4. For a number k, let A = \begin{bmatrix} 1 & 1 & 2 \\ 1 & 0 & 1 \\ 0 & 1 & k \\ 1 & 2 & 3 \end{bmatrix}, \qquad \mathbf{b} = \begin{bmatrix} 4 \\ 1…
6. Let A be an m × n matrix.