The equation is
.
The matrices have the same dimensions and the corresponding elements are equal.
\The equality can be written as a two linear equations
\
Equation (1)
Equation (2)
Equation (3)
The first equation is
.
Apply addition property of equality: if
, then
.
(Add 3 to each side)
(Apply Additive inverse property:
)
(Apply Additive identity property:
)
(Add:
)
Apply division property of equality; if
, then
.
(Divide each side by 4)
(Cancel common terms)
(Divide:
)
The second equation is
.
Apply division property of equality; if
, then
.
(Divide each side by 3)
(Cancel common terms)
(Divide:
)
The third equation is
.
Apply subtraction property of equality: if
, then
.
(Subtract 1 from each side)
(Apply Additive inverse property:
)
(Apply Additive identity property:
)
(Subtract:
)
Apply division property of equality; if
, then
.
(Divide each side by 2)
(Cancel common terms)
(Divide:
)
The solution is
.