To find the correct matrix that represents the given system of equations, we need to express the system in matrix form. The system provided is:
[tex]\[
\begin{array}{rl}
1. & 4x + 5y = 12 \\
2. & 6x - 2y = 15
\end{array}
\][/tex]
For a given system of equations, the matrix representation (often known as the augmented matrix) includes the coefficients of the variables and the constants from the right-hand side of the equations. This is done as follows:
1. Identify the coefficients of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] in both equations.
- For the first equation [tex]\(4x + 5y = 12\)[/tex], the coefficients are 4 and 5, and the constant term is 12.
- For the second equation [tex]\(6x - 2y = 15\)[/tex], the coefficients are 6 and -2, and the constant term is 15.
2. Construct the augmented matrix using these coefficients and constants:
[tex]\[
\left[\begin{array}{ccc}
4 & 5 & 12 \\
6 & -2 & 15
\end{array}\right]
\][/tex]
Thus, the matrix that represents the given system of equations is:
[tex]\[
\left[\begin{array}{ccc}
4 & 5 & 12 \\
6 & -2 & 15
\end{array}\right]
\][/tex]
To match this with the available options:
A. Matrilita
B. Matrix B
C. Matrix C
D. Matrix D
The option that corresponds exactly to our constructed matrix:
[tex]\[
\left[\begin{array}{ccc}
4 & 5 & 12 \\
6 & -2 & 15
\end{array}\right]
\][/tex]
is
[tex]\[
\left[\begin{array}{ccc}
4 & 5 & 12 \\
6 & -2 & 15
\end{array}\right]
\][/tex]
which matches with the answer options provided. Among the options given in the context of the problem, choose the one that matches this matrix explicitly.
