GIVEN: A E M(3,3), a € R. -1) -6 0 2 -4 -2 (a + 6)) Find all values of a so that A¹ does not exist (DNE) A (a −4) 8
GIVEN: A E M(3,3), a € R. -1) -6 0 2 -4 -2 (a + 6)) Find all values of a so that A¹ does not exist (DNE) A (a −4) 8
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**GIVEN:** \( A \in M(3,3), a \in \mathbb{R} \).
\[
A = \begin{pmatrix} (a-1) & -6 & -4 \\ 0 & (a-4) & -2 \\ 2 & 8 & (a+6) \end{pmatrix}
\]
**Find all values of** \( a \) **so that** \( A^{-1} \) **does not exist** (DNE).
To determine when \( A^{-1} \) does not exist, we need to find the values of \( a \) for which the determinant of matrix \( A \) is zero, as a matrix is not invertible when its determinant is zero.
### Explanation:
- **Matrix \( A \):** A 3x3 matrix with elements involving the variable \( a \).
- **Goal:** Identify values of \( a \) such that the determinant of \( A \) equals zero, making \( A \) non-invertible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff74ed3d3-57eb-4d2e-87f6-d577352010e1%2F9c30d10e-1cc7-4596-b825-48773c8479dd%2Fif1apvk_processed.png&w=3840&q=75)
Transcribed Image Text:**GIVEN:** \( A \in M(3,3), a \in \mathbb{R} \).
\[
A = \begin{pmatrix} (a-1) & -6 & -4 \\ 0 & (a-4) & -2 \\ 2 & 8 & (a+6) \end{pmatrix}
\]
**Find all values of** \( a \) **so that** \( A^{-1} \) **does not exist** (DNE).
To determine when \( A^{-1} \) does not exist, we need to find the values of \( a \) for which the determinant of matrix \( A \) is zero, as a matrix is not invertible when its determinant is zero.
### Explanation:
- **Matrix \( A \):** A 3x3 matrix with elements involving the variable \( a \).
- **Goal:** Identify values of \( a \) such that the determinant of \( A \) equals zero, making \( A \) non-invertible.
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