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Which of the values of x and y makes the following matrices equal:
$\left[ \begin{gathered}
  3x + 7\,\,\,\,\,\,5 \\
  y + 1\,\,\,\,\,2 - 3x \\
\end{gathered} \right] = \left[ \begin{gathered}
  0\,\,\,\,\,\,y - 2 \\
  8\,\,\,\,\,\,\,\,\,\,4 \\
\end{gathered} \right]$
A. $x = \dfrac{{ - 1}}{3}$, $y = 7$
B. Not possible to find
C. y = 7, $x = \dfrac{{ - 2}}{3}$
D. $x = \dfrac{{ - 1}}{3},y = \dfrac{{ - 2}}{3}$

Answer Verified Verified
Hint: In order to solve this problem we need to know if two matrices A and B are said to be equal if A and B have the same order and their corresponding elements are equal. Corresponding elements of the matrix A and the matrix B are equal, that is the entries of the matrix A and the matrix B in the same position are equal. Knowing this will solve your problem.

Complete step-by-step answer:
We need to find the values of x and y that can make the following matrices equal:
$\left[ \begin{gathered}
  3x + 7\,\,\,\,\,\,5 \\
  y + 1\,\,\,\,\,2 - 3x \\
\end{gathered} \right] = \left[ \begin{gathered}
  0\,\,\,\,\,\,y - 2 \\
  8\,\,\,\,\,\,\,\,\,\,4 \\
\end{gathered} \right]$
Two matrices A and B are said to be equal if A and B have the same order and their corresponding elements are equal. Corresponding elements of the matrix A and the matrix B are equal, that is the entries of the matrix A and the matrix B in the same position are equal.
So, we do
3x + 7 = 0
So, the value of x is $\dfrac{{ - 7}}{3}$.
If we want to check whether the value of x is correct or not then we will check the last element of the matrices that is 2 – 3x = 4
And here the value of x is $\dfrac{{ - 2}}{3}$.
Therefore x cannot have two values in the same matrices. So it is unable to find the values and finding the value of y is also of no use.
Therefore, the correct answer to this problem is B, not possible to find.

Note:When you get to solve such problems you need to know that one variable cannot have different values in the same matrices. Here we have found two different values so either the matrices are not equal or the matrices given are wrong.