Final answer:
The system of linear equations can be written in matrix form as Ax = b, where A is the coefficient matrix, x is the vector of variables, and b is the vector of constants.
Step-by-step explanation:
To write the given system of linear equations as ax = b, we need to represent it in matrix form. The system of equations given is:
- x1 + 2x2 + 4x3 = 1
- -2x1 - 3x2 - 5x3 = 0
- 2x1 + x2 = -2
We can express this system as Ax = b, where
A is the coefficient matrix of the variables x1, x2, and x3, x is the column vector of the variables, and b is the column vector of the constants:
A =
\(\left[\begin{array}{ccc}
1 & 2 & 4 \\
-2 & -3 & -5 \\
2 & 1 & 0 \\
\end{array}\right]\)
x =
\(\left[\begin{array}{c}
x1 \\
x2 \\
x3 \\
\end{array}\right]\)
b =
\(\left[\begin{array}{c}
1 \\
0 \\
-2 \\
\end{array}\right]\)
Therefore, the matrix equation corresponding to the system is:
\(\left[\begin{array}{ccc}
1 & 2 & 4 \\
-2 & -3 & -5 \\
2 & 1 & 0 \\
\end{array}\right]\)\(\left[\begin{array}{c}
x1 \\
x2 \\
x3 \\
\end{array}\right]\) = \(\left[\begin{array}{c}
1 \\
0 \\
-2 \\
\end{array}\right]\)