Answer:
option A
Step-by-step explanation:
Step 1
X
[tex]x=\left[\begin{array}{ccc}b&a\\4&a\end{array}\right][/tex]
Step 2
2Y
[tex]\left[\begin{array}{ccc}2c&2d\\2a&2b\end{array}\right][/tex]
Step 3
X - 2Y = Z
[tex]2Y=\left[\begin{array}{ccc}b&a\\4&a\end{array}\right]-\left[\begin{array}{ccc}2c&2d\\2a&2b\end{array}\right]=\left[\begin{array}{ccc}a&c\\16&b\end{array}\right][/tex]
Step 4
Four equations are formed
Equation 1
b - 2c = a
Equation 2
a - 2d = c
Equation 3
4 - 2a = 16
-2a = 16 - 4
-2a = 12
a = -6
Equation 4
a -2b = b
-6 - 2b = b
-6 = b + 2b
-6 = 3b
b = -2
Plug values of a and b in equation 1 and 2
b - 2c = a
-2 -2c = -6
-2c = -6 + 2
-2c = -4
c = -4/-2
c = 2
a - 2d = c
-6 -2d = 2
-2d = 2+6
-2d = 8
d = 8/-2
d = -4
