Worksheets — Set 7

Linear algebra · Eigenvalues and orthogonality

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

Warm-up

1. Compute: [9 10; 11 12] + [10 9; 0 13] = ___ 2. Solve Ax = b for A = [[10, 1], [12, 11]], b = [13, 15] ___ 3. Is v = ⟨10, 12⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [8 9; 10 11] + [9 8; 0 12] = ___ 2. Solve Ax = b for A = [[9, 1], [11, 10]], b = [12, 14] ___ 3. Is v = ⟨9, 11⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[10, 9], [8, 12]]) = ___ 5. Eigenvalues of [[9, 0], [0, 10]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [11 12; 13 14] + [12 11; 0 15] = ___ 8. Solve Ax = b for A = [[12, 1], [14, 13]], b = [15, 17] ___

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More written practice

1. Is v = ⟨12, 14⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[13, 12], [11, 15]]) = ___ 3. Eigenvalues of [[12, 0], [0, 13]]: ___ 4. Compute: [14 15; 16 17] + [15 14; 0 18] = ___ 5. Solve Ax = b for A = [[15, 1], [17, 16]], b = [18, 20] ___ 6. Is v = ⟨15, 17⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [25 26; 27 28] + [26 25; 0 29] = ___ 2. Solve Ax = b for A = [[26, 1], [28, 27]], b = [29, 31] ___ 3. Is v = ⟨26, 28⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically