Answer
$a=2,\text{ }b=\dfrac{9}{4},\text{ }c=-1,\text{ }d=0,\text{ }f=\dfrac{1}{2},\text{ }g=-4
$
Work Step by Step
Equating each corresponding elements in the given matrix equation, $
\begin{bmatrix}
4b+2 & -3 & 4d
\\
-4a & 2 & 3
\\
2f-1 & -14 & 1
\end{bmatrix}
=
\begin{bmatrix}
11 & 2c-1 & 0
\\
-8 & 2 & 3
\\
0 & 3g-2 & 1
\end{bmatrix}
,$ and then solving the resulting equation, then
\begin{align*}
4b+2&=11
\\
4b+2-2&=11-2
\\
4b&=9
\\
\dfrac{4b}{4}&=\dfrac{9}{4}
\\
b&=\dfrac{9}{4}
,\\\\\\
-3&=2c-1
\\
-3+1&=2c-1+1
\\
-2&=2c
\\
-\dfrac{2}{2}&=\dfrac{2c}{2}
\\
-1&=c
,\\\\\\
4d&=0
\\
\dfrac{4d}{4}&=\dfrac{0}{4}
\\
d&=0
,\\\\\\
-4a&=-8
\\
\dfrac{-4a}{-4}&=\dfrac{-8}{-4}
\\
a&=2
,\\\\\\
2f-1&=0
\\
2f-1+1&=0+1
\\
2f&=1
\\
\dfrac{2f}{2}&=\dfrac{1}{2}
\\
f&=\dfrac{1}{2}
,\\\\\\
-14&=3g-2
\\
-14+2&=3g-2+2
\\
-12&=3g
\\
-\dfrac{12}{3}&=\dfrac{3g}{3}
\\
-4&=g
.\end{align*}
Hence, $
a=2,\text{ }b=\dfrac{9}{4},\text{ }c=-1,\text{ }d=0,\text{ }f=\dfrac{1}{2},\text{ }g=-4
.$
