Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![The image contains a handwritten set of linear equations intended for conversion into a matrix form. The equations are:
1. \( x - z = 2 \)
2. \( 2x + y = -7 \)
3. \( 5x + y - 2z = -5 \)
The task is to rewrite these equations in the matrix form \( AX = b \).
Matrix form representation:
\[
A = \begin{bmatrix}
1 & 0 & -1 \\
2 & 1 & 0 \\
5 & 1 & -2
\end{bmatrix}, \quad
X = \begin{bmatrix}
x \\
y \\
z
\end{bmatrix}, \quad
b = \begin{bmatrix}
2 \\
-7 \\
-5
\end{bmatrix}
\]
This representation organizes the coefficients of the variables into matrix \( A \), the variables themselves into column matrix \( X \), and the constants on the right side of the equations into column matrix \( b \).](https://content.bartleby.com/qna-images/question/1c6bc774-d9b2-410f-801e-72e713e927fb/d780514e-57d1-4042-a2ae-04d26647b444/s3glvdp_processed.jpeg)
Transcribed Image Text:The image contains a handwritten set of linear equations intended for conversion into a matrix form. The equations are:
1. \( x - z = 2 \)
2. \( 2x + y = -7 \)
3. \( 5x + y - 2z = -5 \)
The task is to rewrite these equations in the matrix form \( AX = b \).
Matrix form representation:
\[
A = \begin{bmatrix}
1 & 0 & -1 \\
2 & 1 & 0 \\
5 & 1 & -2
\end{bmatrix}, \quad
X = \begin{bmatrix}
x \\
y \\
z
\end{bmatrix}, \quad
b = \begin{bmatrix}
2 \\
-7 \\
-5
\end{bmatrix}
\]
This representation organizes the coefficients of the variables into matrix \( A \), the variables themselves into column matrix \( X \), and the constants on the right side of the equations into column matrix \( b \).
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