Worksheets — Set 16

Linear algebra · Vector spaces

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

Warm-up

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⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [17 18; 19 20] + [18 17; 0 21] = ___ 2. Solve Ax = b for A = [[18, 1], [20, 19]], b = [21, 23] ___ 3. Is v = ⟨18, 20⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[19, 18], [17, 21]]) = ___ 5. Eigenvalues of [[18, 0], [0, 19]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [20 21; 22 23] + [21 20; 0 24] = ___ 8. Solve Ax = b for A = [[21, 1], [23, 22]], b = [24, 26] ___

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More written practice

1. Is v = ⟨21, 23⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[22, 21], [20, 24]]) = ___ 3. Eigenvalues of [[21, 0], [0, 22]]: ___ 4. Compute: [23 24; 25 26] + [24 23; 0 27] = ___ 5. Solve Ax = b for A = [[24, 1], [26, 25]], b = [27, 29] ___ 6. Is v = ⟨24, 26⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [34 35; 36 37] + [35 34; 0 38] = ___ 2. Solve Ax = b for A = [[35, 1], [37, 36]], b = [38, 40] ___ 3. Is v = ⟨35, 37⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Stretch

1. Compute: [42 43; 44 45] + [43 42; 0 46] = ___ 2. Solve Ax = b for A = [[43, 1], [45, 44]], b = [46, 48] ___

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Parent tip: Row-reduce systematically