Use Cramer's rule to solve the following
2x+3y-z=1
To solve the equation using Cramer's rule, we need to find the determinants of the coefficients of x, y, and z, and their respective values in the equation.
The given equation is:
2x + 3y - z = 1
To use Cramer's rule, we need to write the equation in matrix form.
Coefficients matrix (A):
| 2 3 -1 |
Constants matrix (B):
| 1 |
Now, we need to find the determinant of the coefficients matrix (A).
det(A) = | 2 3 -1 |
| 0 0 0 |
| 0 0 0 |
The determinant of A is calculated as follows:
2(0x0 - 0x0) - 3(0x0 - 0x0) - (-1)(0x0 - 0x0)
= 0 - 0 - 0
= 0
If the determinant of A is 0, Cramer's rule cannot be applied, and the system of equations either has no solution or infinitely many solutions.
Therefore, in this case, Cramer's rule is not applicable.