Worksheets — Set 18
Linear algebra · Vector spaces
Print and write your answers. Use diagrams to show thinking.
Warm-up
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⟩}? ___
_See printable PDF for diagram._
Written practice
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⟩}? ___ 4. Find det([[21, 20], [19, 23]]) = ___ 5. Eigenvalues of [[20, 0], [0, 21]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [22 23; 24 25] + [23 22; 0 26] = ___ 8. Solve Ax = b for A = [[23, 1], [25, 24]], b = [26, 28] ___
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More written practice
1. Is v = ⟨23, 25⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[24, 23], [22, 26]]) = ___ 3. Eigenvalues of [[23, 0], [0, 24]]: ___ 4. Compute: [25 26; 27 28] + [26 25; 0 29] = ___ 5. Solve Ax = b for A = [[26, 1], [28, 27]], b = [29, 31] ___ 6. Is v = ⟨26, 28⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___
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Patterns and rules
1. Compute: [36 37; 38 39] + [37 36; 0 40] = ___ 2. Solve Ax = b for A = [[37, 1], [39, 38]], b = [40, 42] ___ 3. Is v = ⟨37, 39⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___
_See printable PDF for diagram._
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Stretch
1. Compute: [44 45; 46 47] + [45 44; 0 48] = ___ 2. Solve Ax = b for A = [[45, 1], [47, 46]], b = [48, 50] ___
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Parent tip: Row-reduce systematically