Question

Which linear system has this matrix of constants? `[[12],[11],[4]]` a, b, c or d
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Answer 1

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,

$\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right]$ $\left[\begin{array}{}x&y&z\end{array}\right]$ = $\left[\begin{array}{}12&11&4\end{array}\right]$

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,

$\left[\begin{array}{}26&17&23\end{array}\right]$ which is not the desired matrix.

Similarly, the linear systems in the options B and C contain the matrix $\left[\begin{array}{}23&17&26\end{array}\right]$ and the matrix  $\left[\begin{array}{}4&11&12\end{array}\right]$ on the RHS of the equality, which are not desired.

Thus, option D is correct.

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