CS223 · Chapter 3 · Annotated SlidesIntroduction to Determinants
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Introduction to Determinants

The 2×2 and 3×3 determinant, minors and cofactors, cofactor expansion along any row or column, and the determinant of a triangular matrix.

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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 15 slides
  1. 1 CS 223: Computational Linear Algebra
  2. 2 Determinants
  3. 3 Slide 3
  4. 4 Cofactor Expansion
  5. 5 Slide 5
  6. 6 Slide 6
  7. 7 Example
  8. 8 Determinant of a Triangular Matrix
  9. 9 Slide 9
  10. 10 Slide 10
  11. 11 Slide 11
  12. 12 Practice problem 1
  13. 13 Practice problem 2
  14. 14 Practice problem 3
  15. 15 Practice problem 4
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CS 223: Computational Linear Algebra

Slide 1: CS 223: Computational Linear Algebra
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Determinants

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Cofactor Expansion

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Notes

  1. det A = Σ aᵢⱼCᵢⱼ along any row or column, with cofactor Cᵢⱼ = (−1)^(i+j) det Aᵢⱼ. Expand along the row/column with the most zeros.

Exam angle

Past exam · Major 2 (251)

Related question: this topic is examined

Past exam · Final (231)

Related question: this topic is examined

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Example

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Determinant of a Triangular Matrix

Slide 8: Determinant of a Triangular Matrix

Notes

  1. Triangular matrix: det = product of the diagonal entries.

Exam angle

PredictionQ1

det of [[2, 5, 1], [0, 3, 7], [0, 0, −1]] is:

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Practice problem 1

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Practice problem 2

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Practice problem 3

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Practice problem 4

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