Worksheets — Set 10

Linear algebra · Eigenvalues and orthogonality

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

Warm-up

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⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [11 12; 13 14] + [12 11; 0 15] = ___ 2. Solve Ax = b for A = [[12, 1], [14, 13]], b = [15, 17] ___ 3. Is v = ⟨12, 14⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[13, 12], [11, 15]]) = ___ 5. Eigenvalues of [[12, 0], [0, 13]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [14 15; 16 17] + [15 14; 0 18] = ___ 8. Solve Ax = b for A = [[15, 1], [17, 16]], b = [18, 20] ___

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More written practice

1. Is v = ⟨15, 17⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[16, 15], [14, 18]]) = ___ 3. Eigenvalues of [[15, 0], [0, 16]]: ___ 4. Compute: [17 18; 19 20] + [18 17; 0 21] = ___ 5. Solve Ax = b for A = [[18, 1], [20, 19]], b = [21, 23] ___ 6. Is v = ⟨18, 20⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [28 29; 30 31] + [29 28; 0 32] = ___ 2. Solve Ax = b for A = [[29, 1], [31, 30]], b = [32, 34] ___ 3. Is v = ⟨29, 31⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically