Worksheets — Set 11

Linear algebra · Eigenvalues and orthogonality

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

Warm-up

1. Compute: [13 14; 15 16] + [14 13; 0 17] = ___ 2. Solve Ax = b for A = [[14, 1], [16, 15]], b = [17, 19] ___ 3. Is v = ⟨14, 16⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [12 13; 14 15] + [13 12; 0 16] = ___ 2. Solve Ax = b for A = [[13, 1], [15, 14]], b = [16, 18] ___ 3. Is v = ⟨13, 15⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[14, 13], [12, 16]]) = ___ 5. Eigenvalues of [[13, 0], [0, 14]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [15 16; 17 18] + [16 15; 0 19] = ___ 8. Solve Ax = b for A = [[16, 1], [18, 17]], b = [19, 21] ___

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More written practice

1. Is v = ⟨16, 18⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[17, 16], [15, 19]]) = ___ 3. Eigenvalues of [[16, 0], [0, 17]]: ___ 4. Compute: [18 19; 20 21] + [19 18; 0 22] = ___ 5. Solve Ax = b for A = [[19, 1], [21, 20]], b = [22, 24] ___ 6. Is v = ⟨19, 21⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [29 30; 31 32] + [30 29; 0 33] = ___ 2. Solve Ax = b for A = [[30, 1], [32, 31]], b = [33, 35] ___ 3. Is v = ⟨30, 32⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically