Its 4x 4
Find
5a + 3c = d
4b - c = d
also
(3a + 2c )/2 = d
Now find
c+ d = -a + 2b
c+ d= 4b
Then
-a + 2b= 4b
a= -2b
So reduce to 3x3 system
2a + c + d = 0
3a + 2c - 2d= 0
5a + 3c - d= 0
Add equations 1 and 3, to get
7a +4c = 0
and equations 2 and 3 ( multiplied by 2), to get
13a + 8c = 0
Now solve 2x2 system
7a +4c = 0
13a + 8c = 0
Solution is a= 0, c =0
Now find b and d
d= 2b
Then solutions are
a= -2b
d= 2b
c= 2b