CS223 · Annotated Slides · Chapter 4

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dim H = number of vectors in any basis of H.

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rank A = dim Col A = dim Row A = number of pivots. Rank Theorem: rank A + dim Nul A = n.

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🎯 How this can come up · 2 questions

MCQ

A 6×9 matrix has a 4-dimensional null space. Its rank is:

True / False

rank A = rank Aᵀ.

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Recall that a coordinate vector is a vector of the weights of a linear combination of the basis to give a certain vector We can generate the same vector using different basis.

Therefore, the weights of the linear combination will be different for the different basis

9

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Dimension and Rank