Worksheets — Set 1

Linear algebra · Vector spaces

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

Warm-up

1. Compute: [3 4; 5 6] + [4 3; 0 7] = ___ 2. Solve Ax = b for A = [[4, 1], [6, 5]], b = [7, 9] ___ 3. Is v = ⟨4, 6⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [2 3; 4 5] + [3 2; 0 6] = ___ 2. Solve Ax = b for A = [[3, 1], [5, 4]], b = [6, 8] ___ 3. Is v = ⟨3, 5⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[4, 3], [2, 6]]) = ___ 5. Eigenvalues of [[3, 0], [0, 4]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [5 6; 7 8] + [6 5; 0 9] = ___ 8. Solve Ax = b for A = [[6, 1], [8, 7]], b = [9, 11] ___

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More written practice

1. Is v = ⟨6, 8⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[7, 6], [5, 9]]) = ___ 3. Eigenvalues of [[6, 0], [0, 7]]: ___ 4. Compute: [8 9; 10 11] + [9 8; 0 12] = ___ 5. Solve Ax = b for A = [[9, 1], [11, 10]], b = [12, 14] ___ 6. Is v = ⟨9, 11⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

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._

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Parent tip: Row-reduce systematically