Coordinates in a Basis and Change of Basis Worksheet with Answer Key

What's on the worksheet

1. Let B = \b_1, b_2, b_3\, where b_1 = (1, -1, -2), b_2 = (-2, 3, 5) and b_3 = (2, 0, -1).
2. A basis B = \b_1, b_2, b_3\ of R³ is not shown, but you are told P_{\mathcal{B}}^{-1} = \begin{bmatrix} 0 & -2 & 1 \\ 2 & 3 & -2 \\ -1 & -1 & 1…
3. Let B = \(-4, -7),\ (-1, -2)\ and C = \(-2, -3),\ (1, 1)\, two bases of R².
4. Let B = \(1, 1, 2),\ (1, 1, 1),\ (1, 0, 2)\ and C = \(1, 0, 1),\ (2, 1, 2),\ (0, 1, 1)\, two bases of R³.
5. Let V = span\b_1, b_2\ in R^4, where b_1 = (1, 0, 2, 1) and b_2 = (0, 1, -1, 1), with basis B = \b_1, b_2\.
6. Let T(x) = Ax, where A = \begin{bmatrix} 0 & 2 \\ -3 & 5 \end{bmatrix}, and let B = \(1, 1),\ (1, 2)\.
7. Daniel feeds a small hydroponic grow rack from stock solutions.