Answer:
[tex]\left[\begin{array}{ccccc}1&0&2&0&:5\\0&1&0&-3&:3\\0&0&1&-2&:5\\0&0&0&\frac{-1}{4} &:-2\end{array}\right][/tex]
Explanation
A. The system is consistent because the augmented matrix of the system can be reduced to triangular form.
Step-by-step explanation:
It can be reduced by triangular form using Row reduction method.
[tex]\left[\begin{array}{ccccc}1&0&2&0&5\\0&1&0&-3&3\\0&-2&2&2&4\\2&0&0&9&-12\end{array}\right][/tex]
The solution is in the attachment.
Thus the option C which is the system is consistent because the augmented matrix of the system can be reduced to triangular form.
Given-
The equations of the given system are,
[tex]x_1+2x_3=5[/tex]
[tex]-3x_4+3[/tex]
[tex]-2x_2+2x_3+2x_4=4[/tex]
[tex]2x_1+9x_4=-2[/tex]
A system will be consistent if the augmented the rank of it is must be large than the rank of the matrix of coefficients.
To check its consistency and the correct option write the equation in the matrix form.
Here we have four variables thus the matrix for the given equation is,
[tex]\begin{bmatrix} 1 &0 & 2 & 0 & 5\\0 &1 & 0 & -3 & 3 \\0&-2&2&2&4\\2& 0&0&9&-12 \end{bmatrix}[/tex]
This matrix can be reduced to by triangular form using the row reduction method. The final matrix after performing the row reduction operation is,
[tex]\begin{bmatrix} 1 &0 & 2 & 0 & 5\\0 &1 & 0 & -3 & 3 \\0&0&1&-2&5\\0& 0&0&\dfrac{-1}{4} &-2 \end{bmatrix}[/tex]
Thus the option C which is the system is consistent because the augmented matrix of the system can be reduced to triangular form.
For more about the matrix follow the link below-
https://brainly.com/question/4470545
