https://file.aiquickdraw.com/mathbot/file/17264536611914lhybvcx.jpg

The task asks to find the inverse of matrix \( A \) using OBE (Operasi Baris Elementer), which is Elementary Row Operations in English.

The matrix \( A \) is given as:

\[
A = \begin{pmatrix} 
4 & -2 & 1 \\ 
-7 & 4 & -2 \\ 
5 & -3 & 2 
\end{pmatrix}
\]

To find the inverse of a matrix using elementary row operations (Gaussian elimination), we augment matrix \( A \) with the identity matrix \( I \) and then apply row operations to transform \( A \) into the identity matrix. Once \( A \) becomes the identity matrix, the augmented matrix will be the inverse of \( A \).

Let me compute the inverse using these steps.The inverse of the matrix \( A \) using Elementary Row Operations (Operasi Baris Elementer) is:

\[
A^{-1} = \begin{pmatrix} 
2 & 1 & 0 \\ 
4 & 3 & 1 \\ 
1 & 2 & 2 
\end{pmatrix}
\]

Would you like further details on the steps or have any questions?

Here are 5 related questions to explore further:
1. How is the determinant of a matrix related to its invertibility?
2. What are the types of Elementary Row Operations in Gaussian elimination?
3. How does Gaussian elimination differ from other methods of finding a matrix inverse?
4. Can the inverse of any matrix be found using Elementary Row Operations?
5. What are some practical applications of finding the inverse of a matrix?

**Tip:** The inverse of a matrix only exists if the matrix is non-singular, meaning its determinant is not zero.

Cari Invers untuk Matriks menggunakan OBE (Operasi Baris Elementer). A = [[4, -2, 1], [-7, 4, -2], [5, -3, 2]]

Learn how to find the inverse of a 3x3 matrix using OBE (Operasi Baris Elementer) or Elementary Row Operations. The matrix A = [[4, -2, 1], [-7, 4, -2], [5, -3, 2]] is solved step-by-step using Gaussian elimination and elementary row operations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation