Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Why did I get -1 when it should be 1 for the inverse of A? what did i do wrong?
**Matrix Inversion Example** **Objective:** Determine the inverse of matrix \(A\). **Given:** \[ A = \begin{bmatrix} 1 & 2 & 0 \\ 0 & 3 & 0 \\ 1 & 0 & 6 \end{bmatrix} \] **Steps:** 1. **Calculate the Determinant of \(A\):** - Find determinant \(|A|\): \[ |A| = 6(-6) = -36 \] - Simplified determinant: \[ |A| = 6 \] 2. **Form the Matrix \(N\):** - Simplified form: \[ N = \begin{bmatrix} 0 & -2 & -6 \\ 3 & 0 & -3 \\ 0 & 2 & 0 \end{bmatrix} \] 3. **Further Simplify Matrix \(N\):** - Switch rows for determinant calculation: \[ N = \begin{bmatrix} 0 & -3 & 0 \\ 2 & 0 & -2 \\ 6 & 3 & 0 \end{bmatrix} \] - Reduction and simplification: \[ N = \begin{bmatrix} 0 & 3 & 0 \\ -2 & 0 & 2 \\ -6 & -3 & 0 \end{bmatrix} \] 4. **Compute the Inverse of \(A\):** - Formula: \[ A^{-1} = \frac{1}{|A|}[N] \] - Calculation: \[ A^{-1} = \frac{1}{6} \begin{bmatrix} 0 & -2 & -6 \\ 3 & 0 & -3 \\ 0 & 2 & 0 \end{bmatrix} \] - Result: \[ A^{-1} = \begin{bmatrix} 0 & -1/3 & 0 \\ 1/2 & 0 & -1/2 \\ 0 & 1/3 & 0 \end{bmatrix} \] **Conclusion:** - The inverse of matrix \(A\) is \(\begin{
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Transcribed Image Text:**Matrix Inversion Example** **Objective:** Determine the inverse of matrix \(A\). **Given:** \[ A = \begin{bmatrix} 1 & 2 & 0 \\ 0 & 3 & 0 \\ 1 & 0 & 6 \end{bmatrix} \] **Steps:** 1. **Calculate the Determinant of \(A\):** - Find determinant \(|A|\): \[ |A| = 6(-6) = -36 \] - Simplified determinant: \[ |A| = 6 \] 2. **Form the Matrix \(N\):** - Simplified form: \[ N = \begin{bmatrix} 0 & -2 & -6 \\ 3 & 0 & -3 \\ 0 & 2 & 0 \end{bmatrix} \] 3. **Further Simplify Matrix \(N\):** - Switch rows for determinant calculation: \[ N = \begin{bmatrix} 0 & -3 & 0 \\ 2 & 0 & -2 \\ 6 & 3 & 0 \end{bmatrix} \] - Reduction and simplification: \[ N = \begin{bmatrix} 0 & 3 & 0 \\ -2 & 0 & 2 \\ -6 & -3 & 0 \end{bmatrix} \] 4. **Compute the Inverse of \(A\):** - Formula: \[ A^{-1} = \frac{1}{|A|}[N] \] - Calculation: \[ A^{-1} = \frac{1}{6} \begin{bmatrix} 0 & -2 & -6 \\ 3 & 0 & -3 \\ 0 & 2 & 0 \end{bmatrix} \] - Result: \[ A^{-1} = \begin{bmatrix} 0 & -1/3 & 0 \\ 1/2 & 0 & -1/2 \\ 0 & 1/3 & 0 \end{bmatrix} \] **Conclusion:** - The inverse of matrix \(A\) is \(\begin{
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