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MatricesLinear algebraCollegeabout 0:42

Find the determinant of [[2,-5,-5],[4,-8,-7],[8,1,8]]: animated lesson

A narrated, step-by-step matrices video lesson with captions. Final answer: det(A) = -14.

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⁡[2−5−54−8−7818]\det \begin{bmatrix}2 & -5 & -5 \\ 4 & -8 & -7 \\ 8 & 1 & 8\end{bmatrix}
  2. 2. Step by step
    1. A=[2−5−54−8−7818]A = \begin{bmatrix}2 & -5 & -5 \\ 4 & -8 & -7 \\ 8 & 1 & 8\end{bmatrix}
      Read the 3×3 matrix
    2. det⁡A=(2)∣−8−718∣−(−5)∣4−788∣+(−5)∣4−881∣\det A = (2)\begin{vmatrix}-8 & -7 \\ 1 & 8\end{vmatrix} - (-5)\begin{vmatrix}4 & -7 \\ 8 & 8\end{vmatrix} + (-5)\begin{vmatrix}4 & -8 \\ 8 & 1\end{vmatrix}
      Expand along the first row (cofactor expansion)
    3. M11=−57,M12=88,M13=68M_{11} = -57,\quad M_{12} = 88,\quad M_{13} = 68
      Evaluate each 2×2 minor
    4. det⁡A=(2)(−57)−(−5)(88)+(−5)(68)=−14\det A = (2)(-57) - (-5)(88) + (-5)(68) = -14
      Combine with the alternating signs + − +
  3. 3. The answer
    det⁡A=−14\det A = -14

    det = -14

  4. 4. Check
    • Computed exactly with fractions; row reduction gives the same value -14.

Transcript

The problem. Here is the problem: [[2, negative 5, negative 5], [4, negative 8, negative 7], [8, 1, 8]]. 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 14. The determinant is negative 14, 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 14.

About matrices

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

More lessons like this

Find the determinant of [[2,-5,-5],[4,-8,-7],[8,1,8]]