How do I solve this? This is confusing.
Solve the system using matrices.
-3x - y - 2z = -389x + 9z = 1172y + z = 16
Here is a Gauss Jordan calculator
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
-3 -1 -2 16
-389 0 9 16
0 1172 1 16
To solve the system of equations using matrices, we can represent the coefficients of the variables in matrix form.
First, rewrite the system of equations in matrix form:
[-3 -1 -2] [x] [-38]
[ 3 0 9] * [y] = [117]
[ 0 2 1] [z] [ 16]
The matrix on the left side represents the coefficients of the variables (x, y, z). The column on the right side represents the constants on the right side of the equations.
To solve this system, we need to find the inverse of the coefficient matrix and then multiply it by the column matrix of constants. The resulting product will give us the values of x, y, and z.
1. Find the inverse of the coefficient matrix:
- First, calculate the determinant of the coefficient matrix.
- If the determinant is non-zero, then the matrix is invertible.
- Calculate the inverse of the coefficient matrix using the formula: inverse = (1/determinant) * adjoint, where the adjoint is the transpose of the matrix of cofactors.
2. Multiply the inverse of the coefficient matrix by the column matrix of constants:
- Multiply the inverse of the coefficient matrix by the column matrix of constants using matrix multiplication.
The resulting product will give you the values of x, y, and z, which are the solutions to the system of equations.