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Find the determinant of [[1,2],[3,4]]: animated lesson

A narrated, step-by-step matrices video lesson with captions. Final answer: det(A) = -2.

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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
$\det \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$
2. Step by step
1. $A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$
  Read the 2×2 matrix
2. $\det A = (1)(4) - (2)(3) = 4 - (6) = -2$
  Use ad − bc for a 2×2 matrix
3. The answer
$\det A = -2$
det = -2
4. Check
- Computed exactly with fractions; row reduction gives the same value -2.

Transcript

The problem. Here is the problem: [[1, 2], [3, 4]]. Find the determinant of a 2 times 2 matrix.

Step by step. Read the 2 times 2 matrix. Use ad minus bc for a 2 times 2 matrix.

The answer. So the answer is det(A) equals negative 2. The determinant is negative 2, which is non-zero, so the matrix is invertible and its rows are linearly independent.

Check. Computed exactly with fractions; row reduction gives the same value negative 2.

About matrices

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

Find the determinant of [[1,2],[3,4]]: Matrices Lesson