Heir it is solved.
Throught the inverse matrix.
I need to find if
3
-1
2
is a linear combination of
1 3 2
-1 1 2
2 -2 -4
I set it up so i had 3 equations they were
3 = x1 + 3x2 +2x3
-1 = -x1 + x2 + 2x3
2 = 2x1 - 2x2 - 4x3
where x1, x2, and x3 are variables. I should be able to solve these and then find the values of the variables and those are the #'s which will make the linear combination possible. But I can't figure it out!!! Help!!!
So you have changed the task that needs to be done from
solving a set of three linear simultaneous equations to that
of inverting a 3x3 matrix. Other than that you have given the
inverse, so having effectively given the answer, you leave the
OP with a task they are less likely to be able to do.
RonL
Replace the second equation by the second plus the first, give us:
Now replace the third row by the third row minus twice the firstCode:3 = x1 + 3.x2 +2.x3 2 = + 4.x2 +4.x3 2 = 2.x1 - 2.x2 - 4.x3
row:
Now we see that the last two rows are multiples of one another,Code:3 = x1 + 3,x2 +2.x3 2 = + 4.x2 +4.x3 -4 = - 8.x2 - 8.x3
which leaves us with two effective equations in three unknowns.
This leaves us with multiple solutions so assume a value for x3
and then solve for x1 and x2 in terms of this.
For instance x1=3/2, x2=1/2, x3=0 looks like a solution to me
(assuming no arithmetic errors).
RonL
Ignore it, first he has inverted the wrong matrix, second the matrix
he should have inverted is singular, third even if the matrix was not
singular he is replacing a simple process related to Gaussian elimination
by a more complex problem without showing how to solve the new
problem.
RonL