Worksheets — Set 9

Linear algebra · Eigenvalues and orthogonality

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

Warm-up

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⟩}? ___

_See printable PDF for diagram._

Written practice

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⟩}? ___ 4. Find det([[12, 11], [10, 14]]) = ___ 5. Eigenvalues of [[11, 0], [0, 12]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [13 14; 15 16] + [14 13; 0 17] = ___ 8. Solve Ax = b for A = [[14, 1], [16, 15]], b = [17, 19] ___

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More written practice

1. Is v = ⟨14, 16⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[15, 14], [13, 17]]) = ___ 3. Eigenvalues of [[14, 0], [0, 15]]: ___ 4. Compute: [16 17; 18 19] + [17 16; 0 20] = ___ 5. Solve Ax = b for A = [[17, 1], [19, 18]], b = [20, 22] ___ 6. Is v = ⟨17, 19⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [27 28; 29 30] + [28 27; 0 31] = ___ 2. Solve Ax = b for A = [[28, 1], [30, 29]], b = [31, 33] ___ 3. Is v = ⟨28, 30⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically