CS223 · Chapter 4 · Annotated SlidesDimension and Rank
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Dimension and Rank

Dimension of a vector space, dimensions of Nul A, Col A and Row A, rank, the Rank Theorem, and rank in the Invertible Matrix Theorem.

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Every original slide is shown unchanged. Yellow marks on a slide point to a numbered note: hover or tap a mark to jump to its note, and hover a note to see its marks. Questions tagged Past exam appeared on a real paper; Prediction questions are likely angles, not confirmed. Pick an answer to each question: a wrong pick tells you why it is wrong, so you can try again.

All 11 slides
  1. 1 Slide 1
  2. 2 Find dim H
  3. 3 Slide 3
  4. 4 Slide 4
  5. 5 The rank of a matrix is
  6. 6 Slide 6
  7. 7 Slide 7
  8. 8 Slide 8
  9. 9 Recall that a coordinate vector is a vector of the weights of a
  10. 10 Slide 10
  11. 11 Slide 11
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Find dim H

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The rank of a matrix is

Slide 5: The rank of a matrix is

Notes

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

Exam angle

Past exam · Major 2 (251)

Related question: this topic is examined

Past exam · Final (231)

Related question: this topic is examined

PredictionQ1

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

PredictionQ2

rank A = rank Aᵀ.

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Recall that a coordinate vector is a vector of the weights of a

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