Worksheets — Set 2

Linear algebra · Systems and matrix algebra

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

Warm-up

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⟩}? ___

_See printable PDF for diagram._

Written practice

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⟩}? ___ 4. Find det([[5, 4], [3, 7]]) = ___ 5. Eigenvalues of [[4, 0], [0, 5]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [6 7; 8 9] + [7 6; 0 10] = ___ 8. Solve Ax = b for A = [[7, 1], [9, 8]], b = [10, 12] ___

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More written practice

1. Is v = ⟨7, 9⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[8, 7], [6, 10]]) = ___ 3. Eigenvalues of [[7, 0], [0, 8]]: ___ 4. Compute: [9 10; 11 12] + [10 9; 0 13] = ___ 5. Solve Ax = b for A = [[10, 1], [12, 11]], b = [13, 15] ___ 6. Is v = ⟨10, 12⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

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._

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Parent tip: Row-reduce systematically