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MatricesLinear algebraCollegeabout 0:40

Find the determinant of [[-7,2,-9],[6,-2,6],[-7,6,0]]: animated lesson

A narrated, step-by-step matrices video lesson with captions. Final answer: det(A) = -30.

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⁡[−72−96−26−760]\det \begin{bmatrix}-7 & 2 & -9 \\ 6 & -2 & 6 \\ -7 & 6 & 0\end{bmatrix}
  2. 2. Step by step
    1. A=[−72−96−26−760]A = \begin{bmatrix}-7 & 2 & -9 \\ 6 & -2 & 6 \\ -7 & 6 & 0\end{bmatrix}
      Read the 3×3 matrix
    2. det⁡A=(−7)∣−2660∣−(2)∣66−70∣+(−9)∣6−2−76∣\det A = (-7)\begin{vmatrix}-2 & 6 \\ 6 & 0\end{vmatrix} - (2)\begin{vmatrix}6 & 6 \\ -7 & 0\end{vmatrix} + (-9)\begin{vmatrix}6 & -2 \\ -7 & 6\end{vmatrix}
      Expand along the first row (cofactor expansion)
    3. M11=−36,M12=42,M13=22M_{11} = -36,\quad M_{12} = 42,\quad M_{13} = 22
      Evaluate each 2×2 minor
    4. det⁡A=(−7)(−36)−(2)(42)+(−9)(22)=−30\det A = (-7)(-36) - (2)(42) + (-9)(22) = -30
      Combine with the alternating signs + − +
  3. 3. The answer
    det⁡A=−30\det A = -30

    det = -30

  4. 4. Check
    • Computed exactly with fractions; row reduction gives the same value -30.

Transcript

The problem. Here is the problem: [[-7, 2, negative 9], [6, negative 2, 6], [-7, 6, 0]]. 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 30. The determinant is negative 30, 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 30.

About matrices

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

More lessons like this

Find the determinant of [[-7,2,-9],[6,-2,6],[-7,6,0]]