Review — Difficulty 7/10

Linear algebra · Eigenvalues and orthogonality

Review skills for this standard. Write answers where shown.

Together with a parent

1. Compute: [11 12; 13 14] + [12 11; 0 15] = ___ 2. Solve Ax = b for A = [[12, 1], [14, 13]], b = [15, 17] ___ 3. Is v = ⟨12, 14⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

Written review

1. Compute: [13 14; 15 16] + [14 13; 0 17] = ___ 2. Solve Ax = b for A = [[14, 1], [16, 15]], b = [17, 19] ___ 3. Is v = ⟨14, 16⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[15, 14], [13, 17]]) = ___ 5. Eigenvalues of [[14, 0], [0, 15]]: ___ 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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