Worksheets — Set 19
Linear algebra · Vector spaces
Print and write your answers. Use diagrams to show thinking.
Warm-up
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⟩}? ___
_See printable PDF for diagram._
Written practice
1. Compute: [20 21; 22 23] + [21 20; 0 24] = ___ 2. Solve Ax = b for A = [[21, 1], [23, 22]], b = [24, 26] ___ 3. Is v = ⟨21, 23⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[22, 21], [20, 24]]) = ___ 5. Eigenvalues of [[21, 0], [0, 22]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [23 24; 25 26] + [24 23; 0 27] = ___ 8. Solve Ax = b for A = [[24, 1], [26, 25]], b = [27, 29] ___
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More written practice
1. Is v = ⟨24, 26⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[25, 24], [23, 27]]) = ___ 3. Eigenvalues of [[24, 0], [0, 25]]: ___ 4. Compute: [26 27; 28 29] + [27 26; 0 30] = ___ 5. Solve Ax = b for A = [[27, 1], [29, 28]], b = [30, 32] ___ 6. Is v = ⟨27, 29⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___
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Patterns and rules
1. Compute: [37 38; 39 40] + [38 37; 0 41] = ___ 2. Solve Ax = b for A = [[38, 1], [40, 39]], b = [41, 43] ___ 3. Is v = ⟨38, 40⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___
_See printable PDF for diagram._
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Stretch
1. Compute: [45 46; 47 48] + [46 45; 0 49] = ___ 2. Solve Ax = b for A = [[46, 1], [48, 47]], b = [49, 51] ___
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Parent tip: Row-reduce systematically