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MatricesLinear algebraCollegeabout 0:42

Find the determinant of [[-5,-5,0],[-9,8,7],[8,-1,-5]]: animated lesson

A narrated, step-by-step matrices video lesson with captions. Final answer: det(A) = 110.

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⁡[−5−50−9878−1−5]\det \begin{bmatrix}-5 & -5 & 0 \\ -9 & 8 & 7 \\ 8 & -1 & -5\end{bmatrix}
  2. 2. Step by step
    1. A=[−5−50−9878−1−5]A = \begin{bmatrix}-5 & -5 & 0 \\ -9 & 8 & 7 \\ 8 & -1 & -5\end{bmatrix}
      Read the 3×3 matrix
    2. det⁡A=(−5)∣87−1−5∣−(−5)∣−978−5∣+(0)∣−988−1∣\det A = (-5)\begin{vmatrix}8 & 7 \\ -1 & -5\end{vmatrix} - (-5)\begin{vmatrix}-9 & 7 \\ 8 & -5\end{vmatrix} + (0)\begin{vmatrix}-9 & 8 \\ 8 & -1\end{vmatrix}
      Expand along the first row (cofactor expansion)
    3. M11=−33,M12=−11,M13=−55M_{11} = -33,\quad M_{12} = -11,\quad M_{13} = -55
      Evaluate each 2×2 minor
    4. det⁡A=(−5)(−33)−(−5)(−11)+(0)(−55)=110\det A = (-5)(-33) - (-5)(-11) + (0)(-55) = 110
      Combine with the alternating signs + − +
  3. 3. The answer
    det⁡A=110\det A = 110

    det = 110

  4. 4. Check
    • Computed exactly with fractions; row reduction gives the same value 110.

Transcript

The problem. Here is the problem: [[-5, negative 5, 0], [-9, 8, 7], [8, negative 1, negative 5]]. 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 110. The determinant is 110, 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 110.

About matrices

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

More lessons like this

Find the determinant of [[-5,-5,0],[-9,8,7],[8,-1,-5]]