Worksheets — Set 15

Linear algebra · Vector spaces

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

Warm-up

1. Compute: [17 18; 19 20] + [18 17; 0 21] = ___ 2. Solve Ax = b for A = [[18, 1], [20, 19]], b = [21, 23] ___ 3. Is v = ⟨18, 20⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [16 17; 18 19] + [17 16; 0 20] = ___ 2. Solve Ax = b for A = [[17, 1], [19, 18]], b = [20, 22] ___ 3. Is v = ⟨17, 19⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[18, 17], [16, 20]]) = ___ 5. Eigenvalues of [[17, 0], [0, 18]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [19 20; 21 22] + [20 19; 0 23] = ___ 8. Solve Ax = b for A = [[20, 1], [22, 21]], b = [23, 25] ___

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More written practice

1. Is v = ⟨20, 22⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[21, 20], [19, 23]]) = ___ 3. Eigenvalues of [[20, 0], [0, 21]]: ___ 4. Compute: [22 23; 24 25] + [23 22; 0 26] = ___ 5. Solve Ax = b for A = [[23, 1], [25, 24]], b = [26, 28] ___ 6. Is v = ⟨23, 25⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [33 34; 35 36] + [34 33; 0 37] = ___ 2. Solve Ax = b for A = [[34, 1], [36, 35]], b = [37, 39] ___ 3. Is v = ⟨34, 36⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically