What are the values of $(x, y, z, t)$, where $3\left[\begin{array}{ll}x & y \\ z & t\end{array}\right]=\left[\begin{array}{cc}x & 6 \\ -1 & 2 t\end{array}\right]+\left[\begin{array}{cc}4 & x+y \\ z+t & 3\end{array}\right]=?$

• A

  $(2,4,3,1)$
• Correct answer
  B

  $(2,4,1,3)$
• C

  $(1,3,2,4)$
• D

  $(1,3,4,2)$

Solution

$3\left[\begin{array}{ll}x & y \\ z & t\end{array}\right]=\left[\begin{array}{cc}x & 6 \\ -1 & 2 t\end{array}\right]+\left[\begin{array}{cc}4 & x+y \\ z+t & 3\end{array}\right]$ $\left[\begin{array}{cc}3 x & 3 y \\ 3 z & 3 t\end{array}\right]=\left[\begin{array}{cc}x+4 & 6+x+y \\ -1+z+t & 2 t+3\end{array}\right]$ On compairing two matrices are equal iff their corresponding elements are equal
$\therefore(x, y, z, t)=(2,4,1,3)$

Hence, the correct answer is option: 'B'.