Worksheets — Set 5

Linear algebra · Eigenvalues and orthogonality

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. Compute: [7 8; 9 10] + [8 7; 0 11] = ___ 2. Solve Ax = b for A = [[8, 1], [10, 9]], b = [11, 13] ___ 3. Is v = ⟨8, 10⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [6 7; 8 9] + [7 6; 0 10] = ___ 2. Solve Ax = b for A = [[7, 1], [9, 8]], b = [10, 12] ___ 3. Is v = ⟨7, 9⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[8, 7], [6, 10]]) = ___ 5. Eigenvalues of [[7, 0], [0, 8]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [9 10; 11 12] + [10 9; 0 13] = ___ 8. Solve Ax = b for A = [[10, 1], [12, 11]], b = [13, 15] ___

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More written practice

1. Is v = ⟨10, 12⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[11, 10], [9, 13]]) = ___ 3. Eigenvalues of [[10, 0], [0, 11]]: ___ 4. Compute: [12 13; 14 15] + [13 12; 0 16] = ___ 5. Solve Ax = b for A = [[13, 1], [15, 14]], b = [16, 18] ___ 6. Is v = ⟨13, 15⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [23 24; 25 26] + [24 23; 0 27] = ___ 2. Solve Ax = b for A = [[24, 1], [26, 25]], b = [27, 29] ___ 3. Is v = ⟨24, 26⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically