Practice Final — Version A

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Question 1 — Determinants, volume, and span

Question 2 — Commuting matrices and a matrix subspace

Question 3 — Kernel and range of a polynomial map

Question 4 — Rank, homogeneous solutions, and matrix maps

Question 5 — Diagonalizability

Question 6 — Changing the input and output bases

Question 7 (3+3+4+5 points) — Distances, angles, and inner products