Solve a problem

MatricesLinear algebraCollegeabout 0:37

Multiply [[1,0,2],[0,1,1]] * [[1,2],[3,4],[5,6]]: animated lesson

A narrated, step-by-step matrices video lesson with captions. Final answer: A × B = [[11, 14], [8, 10]].

SpeedLanguage

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
A × B: A = [[1, 0, 2], [0, 1, 1]]
2. Step by step
1. $A = \begin{bmatrix}1 & 0 & 2 \\ 0 & 1 & 1\end{bmatrix}\ (2×3)$
  Read matrix A
2. $B = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 & 6\end{bmatrix}\ (3×2)$
  Read matrix B
3. $c_{11} = (1)(1) + (0)(3) + (2)(5) = 11$
  Each entry is a row of A dotted with a column of B
4. $\begin{bmatrix}11 & 14 \\ 8 & 10\end{bmatrix}$
  Result
3. The answer
$\begin{bmatrix}11 & 14 \\ 8 & 10\end{bmatrix}$
[[11, 14], [8, 10]]
4. Check
- All arithmetic is exact (fractions, no rounding).

Transcript

The problem. Here is the problem: A times B: A equals [[1, 0, 2], [0, 1, 1]]. Compute A times B exactly.

Step by step. Read matrix A. Read matrix B. Each entry is a row of A dotted with a column of B. The result is 2 times 2. Result.

The answer. So the answer is A times B equals [[11, 14], [8, 10]]. A is 2 times 3 and B is 3 times 2, so AB is 2 times 2. Matrix multiplication is not commutative: BA is generally different.

Check. All arithmetic is exact (fractions, no rounding).

About matrices

Determinants, inverses, products, transposes and eigenvalues of matrices.

Multiply [[1,0,2],[0,1,1]] * [[1,2],[3,4],[5,6]] (Lesson)