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# matrix equation Ax = 0 watch

1. i have been told to find the general solution to the matrix equation Ax = 0 for some 3x3 matrices. what does this really mean? thanks for the help
2. find the vector x that satisifies it. take a general A and you should get three simultaneous equations in terms of the variables x1,x2 and x3 which you then solve for.
3. (Original post by latentcorpse)
find the vector x that satisifies it. take a general A and you should get three simultaneous equations in terms of the variables x1,x2 and x3 which you then solve for.
sorry i am not quite following. does this mean A = the 3x3 matrix and x is the single column matrix:

x1
x2
x3

so i solve the simultaneous equations when they all equal zero? i am still not understanding.
4. HELP ME SOMEONE!!! I NEED TO DO THIS SOON OR ELSE I WILL GET INTO TROUBLE! thanks
5. Could you give me an example of one of the 3x3 matrices you call A
6. (Original post by ian.slater)
Could you give me an example of one of the 3x3 matrices you call A
2 -1 1
4 2 1
-2 1 2

then it tells you solve Ax = 0 for a matrix such as this
7. I get the determinant of your matrix as 24. So I think the only solution is x = (0,0,0).

If the matrix were singular, we could look for non-trivial solutions.
8. (Original post by ian.slater)
I get the determinant of your matrix as 24. So I think the only solution is x = (0,0,0).

If the matrix were singular, we could look for non-trivial solutions.
what about with these other two matrices? is there a solution other than x = (0,0,0). here they are:

-1 1 0
2 -1 -1
1 0 -1

1 -2 1
-1 2 -1
2 -4 2

you have worked them out in the way I said?
9. (Original post by wrooru)
what about with these other two matrices? is there a solution other than x = (0,0,0). here they are:

-1 1 0
2 -1 -1
1 0 -1
is singular, because row 3 - row 2 = row 1

so it's worth looking
10. If you write x as (x,y,z)

This multiplies out to -x + y = 0 etc

You should see that x=y=z is a solution.

so original vector x = (L,L,L) for any value of L
11. Looking at your other matrix, row 1 + row 2 = 0 and row 3 = twice row 1

Singular, hence non-trivial solutions - anything that satisfies x - 2y + z = 0 satisfies all three equations.

(p,q, 2q-p) will work for any p,q

So the first matrix yields a point, the second a line, the third a plane and that's the point of the question

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