Worksheets — Set 20

Linear algebra · Systems and matrix algebra

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

Warm-up

1. Compute: [22 23; 24 25] + [23 22; 0 26] = ___ 2. Solve Ax = b for A = [[23, 1], [25, 24]], b = [26, 28] ___ 3. Is v = ⟨23, 25⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [21 22; 23 24] + [22 21; 0 25] = ___ 2. Solve Ax = b for A = [[22, 1], [24, 23]], b = [25, 27] ___ 3. Is v = ⟨22, 24⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[23, 22], [21, 25]]) = ___ 5. Eigenvalues of [[22, 0], [0, 23]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [24 25; 26 27] + [25 24; 0 28] = ___ 8. Solve Ax = b for A = [[25, 1], [27, 26]], b = [28, 30] ___

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More written practice

1. Is v = ⟨25, 27⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[26, 25], [24, 28]]) = ___ 3. Eigenvalues of [[25, 0], [0, 26]]: ___ 4. Compute: [27 28; 29 30] + [28 27; 0 31] = ___ 5. Solve Ax = b for A = [[28, 1], [30, 29]], b = [31, 33] ___ 6. Is v = ⟨28, 30⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [38 39; 40 41] + [39 38; 0 42] = ___ 2. Solve Ax = b for A = [[39, 1], [41, 40]], b = [42, 44] ___ 3. Is v = ⟨39, 41⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Stretch

1. Compute: [46 47; 48 49] + [47 46; 0 50] = ___ 2. Solve Ax = b for A = [[47, 1], [49, 48]], b = [50, 52] ___

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Parent tip: Row-reduce systematically