| 3 2 7 | x1 | | 46 |
| -2 1 4 | x2 | = | 12 |
| 6 -5 8 | x3 | | 60 |
(b). Solve the system using the inverse of the coefficient matrix.
(x1, x2, x3) = (________)
well, since AX = B,
X = A-1B
X = 1/6 {23,2,29}
The inverse is at
http://www.wolframalpha.com/input/?i=inverse%28{{+3%2C+2%2C+7}%2C+{+-2%2C+1%2C+4}%2C{+6%2C+-5%2C+8}}%29
and the solution is at
http://www.wolframalpha.com/input/?i=inverse%28{{+3%2C+2%2C+7}%2C+{+-2%2C+1%2C+4}%2C{+6%2C+-5%2C+8}}%29*{{46}%2C{12}%2C{60}}
i need the 3 numbers for the answer, how do i find that?
Do you know how to find the inverse of a 3by3 matrix?
I got the following:
28 -51 1
40 -18 -26
4 27 7
each is divided by 192
so multiply the above inverse matrix by
46
12
60
then divide each result by 192 for your x1, x2, x3
aside from the fact that I gave you the three numbers as the vector X, take a look at the 2nd url I gave you.
To solve the system using the inverse of the coefficient matrix, we need to follow these steps:
Step 1: Identify the coefficient matrix and the constant matrix. The coefficient matrix is the matrix with the entries on the left-hand side of the equation, and the constant matrix is the matrix on the right-hand side.
The coefficient matrix:
| 3 2 7 |
| -2 1 4 |
| 6 -5 8 |
The constant matrix:
| 46 |
| 12 |
| 60 |
Step 2: Calculate the inverse of the coefficient matrix. The inverse matrix for a square matrix A can be denoted as A^(-1). Let's denote our coefficient matrix as M. The inverse of M, denoted as M^(-1), can be calculated using various methods such as the Gauss-Jordan elimination method or by using matrix algebra software.
Assuming M^(-1) exists, let's use it to solve the system.
Step 3: Multiply the inverse of the coefficient matrix (M^(-1)) with the constant matrix to solve for the variables x1, x2, and x3. Let's denote the constant matrix as B.
(M^(-1)) * B = (x1, x2, x3)
So, (M^(-1)) * B = (x1, x2, x3)
Step 4: Calculate the product of the inverse of the coefficient matrix and the constant matrix to find the values of x1, x2, and x3.
(x1, x2, x3) = (M^(-1)) * B
By performing these calculations, we can find the values of x1, x2, and x3 by substituting the values into the equation.
Please note that solving the system using the inverse of the coefficient matrix assumes that the inverse exists. If the inverse does not exist, the system may have no unique solution or may be inconsistent.