Worksheets — Set 12

Linear algebra · Eigenvalues and orthogonality

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

Warm-up

1. Compute: [14 15; 16 17] + [15 14; 0 18] = ___ 2. Solve Ax = b for A = [[15, 1], [17, 16]], b = [18, 20] ___ 3. Is v = ⟨15, 17⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

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⟩}? ___ 4. Find det([[15, 14], [13, 17]]) = ___ 5. Eigenvalues of [[14, 0], [0, 15]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [16 17; 18 19] + [17 16; 0 20] = ___ 8. Solve Ax = b for A = [[17, 1], [19, 18]], b = [20, 22] ___

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More written practice

1. Is v = ⟨17, 19⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[18, 17], [16, 20]]) = ___ 3. Eigenvalues of [[17, 0], [0, 18]]: ___ 4. Compute: [19 20; 21 22] + [20 19; 0 23] = ___ 5. Solve Ax = b for A = [[20, 1], [22, 21]], b = [23, 25] ___ 6. Is v = ⟨20, 22⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [30 31; 32 33] + [31 30; 0 34] = ___ 2. Solve Ax = b for A = [[31, 1], [33, 32]], b = [34, 36] ___ 3. Is v = ⟨31, 33⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically