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MatricesLinear algebraCollegeabout 0:45

Find the determinant of [[1,9,-2],[9,-6,0],[-1,4,-5]]: animated lesson

A narrated, step-by-step matrices video lesson with captions. Final answer: det(A) = 375.

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⁡[19−29−60−14−5]\det \begin{bmatrix}1 & 9 & -2 \\ 9 & -6 & 0 \\ -1 & 4 & -5\end{bmatrix}
  2. 2. Step by step
    1. A=[19−29−60−14−5]A = \begin{bmatrix}1 & 9 & -2 \\ 9 & -6 & 0 \\ -1 & 4 & -5\end{bmatrix}
      Read the 3×3 matrix
    2. det⁡A=(1)∣−604−5∣−(9)∣90−1−5∣+(−2)∣9−6−14∣\det A = (1)\begin{vmatrix}-6 & 0 \\ 4 & -5\end{vmatrix} - (9)\begin{vmatrix}9 & 0 \\ -1 & -5\end{vmatrix} + (-2)\begin{vmatrix}9 & -6 \\ -1 & 4\end{vmatrix}
      Expand along the first row (cofactor expansion)
    3. M11=30,M12=−45,M13=30M_{11} = 30,\quad M_{12} = -45,\quad M_{13} = 30
      Evaluate each 2×2 minor
    4. det⁡A=(1)(30)−(9)(−45)+(−2)(30)=375\det A = (1)(30) - (9)(-45) + (-2)(30) = 375
      Combine with the alternating signs + − +
  3. 3. The answer
    det⁡A=375\det A = 375

    det = 375

  4. 4. Check
    • Computed exactly with fractions; row reduction gives the same value 375.

Transcript

The problem. Here is the problem: [[1, 9, negative 2], [9, negative 6, 0], [-1, 4, 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 375. The determinant is 375, 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 375.

About matrices

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

More lessons like this

Find the determinant of [[1,9,-2],[9,-6,0],[-1,4,-5]]