Suppose that you are given the following system of linear equations
[variables are x1, x2, x3 and x4]
x1 + 3x2 + 9x3 + 2x4 =5
x1 + 3x3 - 4x4 =5
x2 + 2x3 + 3x4 =-1
-2x1 + 3x2 + 5x4 =-1
What is the general solution for the system? Write this general solution in
parametric vector form.
i row reduced the augmented matrix into:
1 0 3 0 1
0 1 2 0 2
0 0 0 0 -1
0 0 0 0 0
did i row reduce this matrix correctly?
the solution i got is
x3 is free
I don't really know the difference between general solution and general solution in parametric vector form, can anybody show me the two? thanks.
thanks everybody. There is another part to this question which i don't know how to do.
Let m be the number of linearly independent columns of A, let k be the number of parameters (free variables), and let n be the total number of columns in A. In our example above, n = 4.
Notice that m + k = n. Do you suppose that this relationship will be true for all systems of linear equations? Why or why not?