Worksheets — Set 4

Linear algebra · Eigenvalues and orthogonality

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

Warm-up

1. Compute: [6 7; 8 9] + [7 6; 0 10] = ___ 2. Solve Ax = b for A = [[7, 1], [9, 8]], b = [10, 12] ___ 3. Is v = ⟨7, 9⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

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

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More written practice

1. Is v = ⟨9, 11⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[10, 9], [8, 12]]) = ___ 3. Eigenvalues of [[9, 0], [0, 10]]: ___ 4. Compute: [11 12; 13 14] + [12 11; 0 15] = ___ 5. Solve Ax = b for A = [[12, 1], [14, 13]], b = [15, 17] ___ 6. Is v = ⟨12, 14⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [22 23; 24 25] + [23 22; 0 26] = ___ 2. Solve Ax = b for A = [[23, 1], [25, 24]], b = [26, 28] ___ 3. Is v = ⟨23, 25⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically