x1
+x1
+x1
+x1
+x2
+x2
+x2
+x2
+x3
+x3
+x3
+x3
+x4
=x4
=x4
=x4
=Number format
Solution comments
Without description (answer only)
a
b
c
d
x
y
z
clear
i
Randomize
3131313131351515151515≈83137
How to solve a system by Cramer's rule
Compute the determinant of the coefficient matrix (D). For each unknown xᵢ, replace the i-th column of the coefficient matrix with the constants vector, take that determinant (Dᵢ), and set xᵢ = Dᵢ / D. The system has a unique solution when D ≠ 0.
Cramer's rule worked example (2 equations)
Write the system of equations in matrix form:
3
1
2
-1
5
0
Write the initial matrix
A
:
A
=
3
1
2
-1
Write the initial matrix
B
:
B
=
5
0
x
0
j
=
▲
0
j
▲
;
j
is the column number▲
is the determinant of the matrix A▲ⱼ
is the determinant of the matrix A in which the jth column is replaced by the matrix B2
▲▲ =
3
1
2
-1
=
-5
;
3
▲₁▲
0
1
=
5
0
2
-1
=
-5
;
4
▲₂▲
0
2
=
3
1
5
0
=
-5
;
5
xx
0
1
=
▲
0
1
▲
=
-5
-5
=
=
1
;
x
0
2
=
▲
0
2
▲
=
-5
-5
=
=
1
;
Answer
Ax = bx
0
1
=
1
;
x
0
2
=
1
;
SIZE2×3METHODCramer's rule