X-2=2 2x+y=-7 5x+1-2x = ²5 rewrite in matrix form AX = b
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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![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 \( b \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c6bc774-d9b2-410f-801e-72e713e927fb%2Fd780514e-57d1-4042-a2ae-04d26647b444%2Fs3glvdp_processed.jpeg&w=3840&q=75)
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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