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anonymous

  • 4 years ago

show that the following are spanning sets for R3. {(1,1,1)transpose (1,1,0)transpose (1,0,0)transpose} plz show full solution

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  1. anonymous
    • 4 years ago
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    Put into a matrix and use row-operations to get three linearly independent rows: (1,0,0), (0,1,0) and (0,0,1).

  2. anonymous
    • 4 years ago
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    1 0 0 1 1 0 1 1 1 subtract row 1 from row two: 1 0 0 0 1 0 1 1 1 now subtract row 1 and row 2 from row 3: 1 0 0 0 1 0 0 0 1 we are in reduced row-echeon form, so the three rows must form a linearly independent set which spans \[\mathbb{R}^3\]

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