Worksheets — Set 8

Linear algebra · Systems and matrix algebra

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

Warm-up

1. Compute: [10 11; 12 13] + [11 10; 0 14] = ___ 2. Solve Ax = b for A = [[11, 1], [13, 12]], b = [14, 16] ___ 3. Is v = ⟨11, 13⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [9 10; 11 12] + [10 9; 0 13] = ___ 2. Solve Ax = b for A = [[10, 1], [12, 11]], b = [13, 15] ___ 3. Is v = ⟨10, 12⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[11, 10], [9, 13]]) = ___ 5. Eigenvalues of [[10, 0], [0, 11]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [12 13; 14 15] + [13 12; 0 16] = ___ 8. Solve Ax = b for A = [[13, 1], [15, 14]], b = [16, 18] ___

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More written practice

1. Is v = ⟨13, 15⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[14, 13], [12, 16]]) = ___ 3. Eigenvalues of [[13, 0], [0, 14]]: ___ 4. Compute: [15 16; 17 18] + [16 15; 0 19] = ___ 5. Solve Ax = b for A = [[16, 1], [18, 17]], b = [19, 21] ___ 6. Is v = ⟨16, 18⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [26 27; 28 29] + [27 26; 0 30] = ___ 2. Solve Ax = b for A = [[27, 1], [29, 28]], b = [30, 32] ___ 3. Is v = ⟨27, 29⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically