Worksheets — Set 3

Linear algebra · Vector spaces

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

Warm-up

1. Compute: [5 6; 7 8] + [6 5; 0 9] = ___ 2. Solve Ax = b for A = [[6, 1], [8, 7]], b = [9, 11] ___ 3. Is v = ⟨6, 8⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [4 5; 6 7] + [5 4; 0 8] = ___ 2. Solve Ax = b for A = [[5, 1], [7, 6]], b = [8, 10] ___ 3. Is v = ⟨5, 7⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[6, 5], [4, 8]]) = ___ 5. Eigenvalues of [[5, 0], [0, 6]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [7 8; 9 10] + [8 7; 0 11] = ___ 8. Solve Ax = b for A = [[8, 1], [10, 9]], b = [11, 13] ___

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More written practice

1. Is v = ⟨8, 10⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[9, 8], [7, 11]]) = ___ 3. Eigenvalues of [[8, 0], [0, 9]]: ___ 4. Compute: [10 11; 12 13] + [11 10; 0 14] = ___ 5. Solve Ax = b for A = [[11, 1], [13, 12]], b = [14, 16] ___ 6. Is v = ⟨11, 13⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

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._

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Parent tip: Row-reduce systematically