The following linear system has [[12], [11], [4]] matrix of constants,
x + y + z = 12
x - y = 11
x - y + z = 4
(Option D)
Verification of the Choice:
The given linear system is,
x + y + z = 12
x - y = 11
x - y + z = 4
This can be written in the form of matrix as follows,
[tex]\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right][/tex] [tex]\left[\begin{array}{}x&y&z\end{array}\right][/tex] = [tex]\left[\begin{array}{}12&11&4\end{array}\right][/tex]
Hence, option D is the correct linear system as it contains the desired matrix.
About the Other Options:
The RHS matrix in option A would be,
[tex]\left[\begin{array}{}26&17&23\end{array}\right][/tex] which is not the desired matrix.
Similarly, the linear systems in the options B and C contain the matrix [tex]\left[\begin{array}{}23&17&26\end{array}\right][/tex] and the matrix [tex]\left[\begin{array}{}4&11&12\end{array}\right][/tex] on the RHS of the equality, which are not desired.
Thus, option D is correct.
Learn more about a matrix here:
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