Can that same method be used for a 3x3 matrix? The image shows the equation involving a matrix and its inverse:The matrix on the left is a \(3 \times 3\) matrix:\[\begin{bmatrix}1 & 1 & -2 \\2 & 3 & -7 \\1 & -2 & 8 \end{bmatrix}\]The \(^{-1}\) exponent indicates the inverse of this matrix. The result on the right side of the equation is another \(3 \times 3\) matrix, which is:\[\begin{bmatrix}0 & 0 & 0 \\0 & 0 & 0 \\0 & 0 & 0 \end{bmatrix}\]This signifies that the inverse of the matrix results in a zero matrix, which suggests the original matrix is singular and non-invertible, as the inverse of a non-singular matrix should result in the identity matrix if calculated correctly.

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Can that same method be used for a 3x3 matrix?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Can that same method be used for a 3x3 matrix?

The image shows the equation involving a matrix and its inverse:

The matrix on the left is a \(3 \times 3\) matrix:
\[
\begin{bmatrix}
1 & 1 & -2 \\
2 & 3 & -7 \\
1 & -2 & 8
\end{bmatrix}
\]

The \(^{-1}\) exponent indicates the inverse of this matrix. The result on the right side of the equation is another \(3 \times 3\) matrix, which is:
\[
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix}
\]

This signifies that the inverse of the matrix results in a zero matrix, which suggests the original matrix is singular and non-invertible, as the inverse of a non-singular matrix should result in the identity matrix if calculated correctly.

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