Worksheets — Set 13

Linear algebra · Vector spaces

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

Warm-up

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⟩}? ___

_See printable PDF for diagram._

Written practice

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⟩}? ___ 4. Find det([[16, 15], [14, 18]]) = ___ 5. Eigenvalues of [[15, 0], [0, 16]]: ___ 6. Interpret a linear transformation geometrically. 7. Compute: [17 18; 19 20] + [18 17; 0 21] = ___ 8. Solve Ax = b for A = [[18, 1], [20, 19]], b = [21, 23] ___

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More written practice

1. Is v = ⟨18, 20⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___ 2. Find det([[19, 18], [17, 21]]) = ___ 3. Eigenvalues of [[18, 0], [0, 19]]: ___ 4. Compute: [20 21; 22 23] + [21 20; 0 24] = ___ 5. Solve Ax = b for A = [[21, 1], [23, 22]], b = [24, 26] ___ 6. Is v = ⟨21, 23⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

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Patterns and rules

1. Compute: [31 32; 33 34] + [32 31; 0 35] = ___ 2. Solve Ax = b for A = [[32, 1], [34, 33]], b = [35, 37] ___ 3. Is v = ⟨32, 34⟩ in span{⟨1,0⟩, ⟨0,1⟩}? ___

_See printable PDF for diagram._

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Parent tip: Row-reduce systematically