Worksheets — Set 17

Linear algebra · Vector spaces

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

Warm-up

1. Compute: [19 20; 21 22] + [20 19; 0 23] = ___ 2. Solve Ax = b for A = [[20, 1], [22, 21]], b = [23, 25] ___ 3. Is v = ⟨20, 22⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [18 19; 20 21] + [19 18; 0 22] = ___ 2. Solve Ax = b for A = [[19, 1], [21, 20]], b = [22, 24] ___ 3. Is v = ⟨19, 21⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[20, 19], [18, 22]]) = ___ 5. Eigenvalues of [[19, 0], [0, 20]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [21 22; 23 24] + [22 21; 0 25] = ___ 8. Solve Ax = b for A = [[22, 1], [24, 23]], b = [25, 27] ___

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More written practice

1. Is v = ⟨22, 24⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[23, 22], [21, 25]]) = ___ 3. Eigenvalues of [[22, 0], [0, 23]]: ___ 4. Compute: [24 25; 26 27] + [25 24; 0 28] = ___ 5. Solve Ax = b for A = [[25, 1], [27, 26]], b = [28, 30] ___ 6. Is v = ⟨25, 27⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [35 36; 37 38] + [36 35; 0 39] = ___ 2. Solve Ax = b for A = [[36, 1], [38, 37]], b = [39, 41] ___ 3. Is v = ⟨36, 38⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Stretch

1. Compute: [43 44; 45 46] + [44 43; 0 47] = ___ 2. Solve Ax = b for A = [[44, 1], [46, 45]], b = [47, 49] ___

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Parent tip: Row-reduce systematically