Worksheets — Set 6

Linear algebra · Eigenvalues and orthogonality

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

Warm-up

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⟩}? ___

_See printable PDF for diagram._

Written practice

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⟩}? ___ 4. Find det([[9, 8], [7, 11]]) = ___ 5. Eigenvalues of [[8, 0], [0, 9]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [10 11; 12 13] + [11 10; 0 14] = ___ 8. Solve Ax = b for A = [[11, 1], [13, 12]], b = [14, 16] ___

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More written practice

1. Is v = ⟨11, 13⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[12, 11], [10, 14]]) = ___ 3. Eigenvalues of [[11, 0], [0, 12]]: ___ 4. Compute: [13 14; 15 16] + [14 13; 0 17] = ___ 5. Solve Ax = b for A = [[14, 1], [16, 15]], b = [17, 19] ___ 6. Is v = ⟨14, 16⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [24 25; 26 27] + [25 24; 0 28] = ___ 2. Solve Ax = b for A = [[25, 1], [27, 26]], b = [28, 30] ___ 3. Is v = ⟨25, 27⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically