# Find x, if $$\begin{bmatrix} 5 & 3x \\ 2y & z \end{bmatrix}$$ = $$\begin{bmatrix} 5 & 4 \\ 12 & 6 \end{bmatrix}^T$$

Toolbox:
• If A_{i,j} be a matrix m*n matrix , then the matrix obtained by interchanging the rows and column of A is called as transpose of A.
• If the order of 2 matrices are equal, their corresponding elements are equal, i.e, if $A_{ij}=B_{ij}$, then any element $a_{ij}$ in matrix A is equal to corresponding element $b_{ij}$ in matrix B.
• We can then match the corresponding elements and solve the resulting equations to find the values of the unknown variables
Step1:
Given:
The transpose of the matrix can be obtained by changing the rows & the column.
${\begin{bmatrix}5 & 4\\12 & 6\end{bmatrix}}^T=\begin{bmatrix}5 & 12\\4 & 6\end{bmatrix}$
Thus $\begin{bmatrix}5 & 3x\\2y & z\end{bmatrix}=\begin{bmatrix}5 & 12\\4 & 6\end{bmatrix}$
The given two matrices are equal,hence their corresponding elements should be equal.
$\Rightarrow$ 3x=12
x=4.
2y=4
$y=\frac{4}{2}$
y=2.
z=6.