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MatricesLinear algebraCollegeabout 0:44

Find the determinant of [[2,8,-4],[7,8,0],[-9,-9,9]]: animated lesson

A narrated, step-by-step matrices video lesson with captions. Final answer: det(A) = -396.

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 (0.3 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    det⁡[28−4780−9−99]\det \begin{bmatrix}2 & 8 & -4 \\ 7 & 8 & 0 \\ -9 & -9 & 9\end{bmatrix}
  2. 2. Step by step
    1. A=[28−4780−9−99]A = \begin{bmatrix}2 & 8 & -4 \\ 7 & 8 & 0 \\ -9 & -9 & 9\end{bmatrix}
      Read the 3×3 matrix
    2. det⁡A=(2)∣80−99∣−(8)∣70−99∣+(−4)∣78−9−9∣\det A = (2)\begin{vmatrix}8 & 0 \\ -9 & 9\end{vmatrix} - (8)\begin{vmatrix}7 & 0 \\ -9 & 9\end{vmatrix} + (-4)\begin{vmatrix}7 & 8 \\ -9 & -9\end{vmatrix}
      Expand along the first row (cofactor expansion)
    3. M11=72,M12=63,M13=9M_{11} = 72,\quad M_{12} = 63,\quad M_{13} = 9
      Evaluate each 2×2 minor
    4. det⁡A=(2)(72)−(8)(63)+(−4)(9)=−396\det A = (2)(72) - (8)(63) + (-4)(9) = -396
      Combine with the alternating signs + − +
  3. 3. The answer
    det⁡A=−396\det A = -396

    det = -396

  4. 4. Check
    • Computed exactly with fractions; row reduction gives the same value -396.

Transcript

The problem. Here is the problem: [[2, 8, negative 4], [7, 8, 0], [-9, negative 9, 9]]. Find the determinant of a 3 times 3 matrix.

Step by step. Read the 3 times 3 matrix. Expand along the first row (cofactor expansion). Evaluate each 2 times 2 minor. Combine with the alternating signs plus minus +.

The answer. So the answer is det(A) equals negative 396. The determinant is negative 396, 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 396.

About matrices

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

More lessons like this

Find the determinant of [[2,8,-4],[7,8,0],[-9,-9,9]]