Linear Algebra

How to solve

Matrix multiplication composes linear maps: each entry of AB is the dot product of a row of A with a column of B. Row i and column j pair corresponding components and add, producing the (i, j) entry.

Steps

  1. For each position (i, j), take row i of A and column j of B.
  2. Compute that row·column dot product for the entry.
  3. Assemble all four entries into the product matrix.

Example

Multiply [[1, 2], [0, 1]] · [[3, 0], [1, 4]].

  1. Top-left: 1·3 + 2·1 = 5.
  2. Top-right: 1·0 + 2·4 = 8.
  3. Bottom-left: 0·3 + 1·1 = 1.
  4. Bottom-right: 0·0 + 1·4 = 4.
  5. Product: [[5, 8], [1, 4]].

Answer: [[5, 8], [1, 4]]

How to type answers

  • Enter [[a, b], [c, d]] — preview shows the matrix
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