Practice question · Put in order
Order the reasoning to find the dimension of the space spanned by a set of vectors.
- Stack the vectors as rows of a matrix
- Discard the redundant vectors
- Run Gaussian elimination
- The rank is the dimension of the span
- Count the nonzero rows (the rank)
Hints
- Elimination exposes redundancy as zero rows.
- Rank = surviving independent directions.
Show the answer
- Stack the vectors as rows of a matrix
- Run Gaussian elimination
- Count the nonzero rows (the rank)
- Discard the redundant vectors
- The rank is the dimension of the span
Why
Stack, eliminate, count, discard, conclude. Gaussian elimination is a redundancy detector: every zero row it produces was a vector pretending to be new.
Practise Vector Spaces
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