CS223 · Chapter 3 · Annotated SlidesProperties of Determinants
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Properties of Determinants

How row operations change the determinant, computing det by row reduction, det A ≠ 0 ⇔ A invertible, det Aᵀ = det A and det(AB) = det A · det B.

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All 10 slides
  1. 1 Determinant of invertible and noninvertible matrices
  2. 2 Determinant of invertible and noninvertible matrices
  3. 3 Slide 3
  4. 4 Slide 4
  5. 5 Slide 5
  6. 6 Slide 6
  7. 7 Slide 7
  8. 8 Slide 8
  9. 9 Practice problem 1
  10. 10 Practice problem 2
Slide 1 / 10

Determinant of invertible and noninvertible matrices

Slide 1: Determinant of invertible and noninvertible matrices

Notes

  1. Row replacement: det unchanged. Row interchange: det changes sign. Scaling a row by k: det multiplied by k.

  2. Memory trick Replace → same; Swap → minus; Scale by k → times k.

Exam angle

PredictionQ1

If B is A with two rows swapped and det A = 5, det B =

Slide 2 / 10

Determinant of invertible and noninvertible matrices

Slide 2: Determinant of invertible and noninvertible matrices
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Slide 3

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Slide 4

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Slide 5

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Slide 6

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Slide 7

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Slide 8

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Notes

  1. Trap det(A + B) ≠ det A + det B, and det(kA) = kⁿ·det A, not k·det A.

Exam angle

PredictionQ1

A is 3×3 with det A = 2. det(2A) =

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Practice problem 1

Slide 9: Practice problem 1
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Practice problem 2

Slide 10: Practice problem 2