I apologize if I offended anyone, with out even thinking I put a title of Reb out of respect for my fellow Yidden, but I’ll stop.
“I can only try”
In the future feel free to ask any math questions, and please don’t think you are taking advantage- I’m here to help.
Here’s how the rule works, (if you know of anyway that I can attach a PDF file to a post or somehow upload a file somewhere that I can link here please let me know. This is hard to follow without mathematical formatting).
2x + y + z = 3
x + 2y + z = 0
Given the general form of a system of three linear equations with three unknown variables:
ax + by +cz = j,
da + ey + fz = k,
ga + hy + iz = l
put this in matrix form:
a b c
d e f
g h i
(3 x 3 matrix)
multiplied by
x
y
z
(3 x 1 matrix)
equals
j
k
l
(3 x 1 matrix)
x =
the determinant of:
j b c
k e f
l h i
divided by
the determinant of:
a b c
d e f
g h i
(The determinant of a 3 x 3 matrix
a b c
d e f
g h i
For our example:
a = 2, b = 1, c = 1, j = 3
d = 1, e = -1, f = -1, k = 0
g = 1, h = 2, i = 1, l = 0
therefore the determinant of
j b c
k e f
l h i
is the determinant of
3 1 1
0 -1 -1
0 2 1
= 3
the determinant of
a b c
d e f
g h i
is the determinant of
2 1 1
1 -1 -1
1 2 1
= -2 -1 + 2 +1 +4 -1
= 3
therefore x = 3/3 = 1.
Similarly
y =
the determinant of:
a j c
d k f
g l i
divided by
the determinant of:
a b c
d e f
g h i
and
z =
the determinant of:
a b j
d e k
g h l
divided by
the determinant of:
a b c
d e f
g h i
The final results are x = 1, y = -2 and z = 3.
I hope this helps.