Review — Difficulty 8/10

Linear algebra · Eigenvalues and orthogonality

Review skills for this standard. Write answers where shown.

Together with a parent

1. Compute: [12 13; 14 15] + [13 12; 0 16] = ___ 2. Solve Ax = b for A = [[13, 1], [15, 14]], b = [16, 18] ___ 3. Is v = ⟨13, 15⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

Written review

1. Compute: [14 15; 16 17] + [15 14; 0 18] = ___ 2. Solve Ax = b for A = [[15, 1], [17, 16]], b = [18, 20] ___ 3. Is v = ⟨15, 17⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[16, 15], [14, 18]]) = ___ 5. Eigenvalues of [[15, 0], [0, 16]]: ___ 6. Interpret a linear transformation geometrically.

_See printable PDF for diagram._

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Skills checklist

• [ ] Solves linear systems with matrices
• [ ] Computes determinants and inverses when defined
• [ ] Interprets linear maps geometrically
• [ ] Explains Eigenvalues and orthogonality without prompts

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