courses › Linear Algebra

Multiply matrices and compute determinants.

Pen and paper is fine · no calculator needed why?

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Opens at level 42.

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Builds on: Vectors (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Matrix product entry par 20 s not tried yet

  worked example

  A = [[−3, 0, −2], [−3, 4, 9]] and B = [[4, −1], [−5, 8], [2, −4]] (rows listed). What is the entry in row 1, column 2 of AB?

  Answer: 11

  1. Row 1 of A is (−3, 0, −2); column 2 of B is (−1, 8, −4).
  2. (−3) × (−1) + 0 × 8 + (−2) × (−4) = 3 + 0 + 8 = 11.

• 2 × 2 determinant par 11 s not tried yet

  worked example

  What is the determinant of [[8, 4], [6, −2]]?

  Answer: -40

  1. For [[a, b], [c, d]] the determinant is ad − bc.
  2. 8 × (−2) − 4 × 6 = −16 − 24 = −40.

• 3 × 3 determinant par 45 s not tried yet

  worked example

  What is the determinant of [[2, −1, 0], [1, −2, 0], [−2, 1, −3]]?

  Answer: 9

  1. Expand along column 3 (cofactor signs + − +); zero entries drop out.
  2. det = −3 × (2 × (−2) − (−1) × 1)
  3. = −3 × (−3) = 9.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

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