Klein Potter
11/27/2023 · Junior High School
Compute the inverse using row reduction. \( \left[\begin{array}{rr}-1 & -2 \\ -3 & -2\end{array}\right] \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Find the inverse matrix of \( \begin{bmatrix}-1 & -2 \\ -3 & -2\end{bmatrix} \).
Matrices by following steps:
- step0: Find the matrix inverse:
\(\left[\begin{array}{rr}{-1}&{-2}\\{-3}&{-2}\end{array}\right]\)
- step1: Evaluate the determinant:
\(-4\)
- step2: Using the formula:
\(\frac{1}{-\left(-2\right)-\left(-2\left(-3\right)\right)}\times \left[\begin{array}{rr}{-2}&{2}\\{3}&{-1}\end{array}\right]\)
- step3: Evaluate:
\(-\frac{1}{4}\times \left[\begin{array}{rr}{-2}&{2}\\{3}&{-1}\end{array}\right]\)
- step4: Multiply the terms:
\(\left[\begin{array}{rr}{-\frac{1}{4}\left(-2\right)}&{-\frac{1}{4}\times 2}\\{-\frac{1}{4}\times 3}&{-\frac{1}{4}\left(-1\right)}\end{array}\right]\)
- step5: Evaluate:
\(\left[\begin{array}{rr}{\frac{1}{2}}&{-\frac{1}{2}}\\{-\frac{3}{4}}&{\frac{1}{4}}\end{array}\right]\)
The inverse of the matrix \( \begin{bmatrix}-1 & -2 \\ -3 & -2\end{bmatrix} \) is \( \begin{bmatrix}\frac{1}{2} & -\frac{1}{2} \\ -\frac{3}{4} & \frac{1}{4}\end{bmatrix} \).
Quick Answer
The inverse matrix is \( \begin{bmatrix}\frac{1}{2} & -\frac{1}{2} \\ -\frac{3}{4} & \frac{1}{4}\end{bmatrix} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit