To find the value of x, we will have to follow the steps below:
step 1: find the scale factor (f) of the dilation between matrix A and B
This will be achieved by comparing similar members of both matrices.
we can observe that
[tex]\begin{gathered} f=\frac{B_{12}}{A_{12}}=\frac{6}{10}=\frac{3}{5} \\ f=\frac{B_{21}}{A_{11}}=\frac{8.4}{14}=\frac{3}{5} \end{gathered}[/tex]
Thus, the scale factor is 3/5
Step 2: use the scale factor to find the value of x
[tex]\begin{gathered} \frac{B_{11}}{A_{11}}=\frac{x}{4.28}=f \\ \frac{x}{4.28}=\frac{3}{5} \end{gathered}[/tex]
cross-multiply
[tex]x=\frac{3\times4.28}{5}=2.568[/tex]
Hence, the value of x = 2.568
