Write the augmented matrix corresponding to the system of equation.
2a-3b+c=1
-a+b-4c=3
3a-b=2
just add a 3x3 array of zeroes on the right
+2 -3 +1 +1
-1 +1 -4 +3
+3 -1 +0 +2
I assume this is from
|+2 -3 +1| |a| +1
|-1 +1 -4| |b|=+3
|+3 -1 +0| |c| +2
solve for a b and c
google gauss jordan
Yes, Steve's method gives you the inverse matrix as well as the solution
sorry, put 1 on the diagonal, zeros off, to get inverse.
To write the augmented matrix corresponding to the system of equations, we need to arrange the coefficients of the variables and constant terms in a matrix form.
The given system of equations is:
2a - 3b + c = 1 ...(Equation 1)
-a + b - 4c = 3 ...(Equation 2)
3a - b = 2 ...(Equation 3)
First, we arrange the coefficients of the variables (a, b, c) and the constant terms (1, 3, 2) in a matrix, with each equation representing a row. The augmented matrix will have three columns, one for each variable and one for the constant terms:
| 2 -3 1 | 1 |
| -1 1 -4 | 3 |
| 3 -1 0 | 2 |
Here, the left part of the vertical line represents the coefficient matrix, and the right part represents the matrix of constant terms. The vertical line separates the coefficient matrix from the matrix of constant terms, forming the augmented matrix.