Worksheets — Set 14

Linear algebra · Vector spaces

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

Warm-up

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⟩}? ___

_See printable PDF for diagram._

Written practice

1. Compute: [15 16; 17 18] + [16 15; 0 19] = ___ 2. Solve Ax = b for A = [[16, 1], [18, 17]], b = [19, 21] ___ 3. Is v = ⟨16, 18⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 4. Find det([[17, 16], [15, 19]]) = ___ 5. Eigenvalues of [[16, 0], [0, 17]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [18 19; 20 21] + [19 18; 0 22] = ___ 8. Solve Ax = b for A = [[19, 1], [21, 20]], b = [22, 24] ___

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More written practice

1. Is v = ⟨19, 21⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[20, 19], [18, 22]]) = ___ 3. Eigenvalues of [[19, 0], [0, 20]]: ___ 4. Compute: [21 22; 23 24] + [22 21; 0 25] = ___ 5. Solve Ax = b for A = [[22, 1], [24, 23]], b = [25, 27] ___ 6. Is v = ⟨22, 24⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [32 33; 34 35] + [33 32; 0 36] = ___ 2. Solve Ax = b for A = [[33, 1], [35, 34]], b = [36, 38] ___ 3. Is v = ⟨33, 35⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically