SOLUTION: I need the general process of finding a span for a set of vectors. Just a random example: (1,3,2) (3,4,5),(5,1,-4)are our three vectors. this makes the matrix (1,3,2) THe Tran

Question 884562: I need the general process of finding a span for a set of vectors.
Just a random example:
(1,3,2) (3,4,5),(5,1,-4)are our three vectors. this makes the matrix
(1,3,2) THe Transpose of this matrix so that Col1 = (1,3,2)
(3,4,5)
(5,1,-4)
(0,0,0)
and I reduce it and obtain the identity matrix.
What does that imply?
and if it isn't the matrix I, how do i go about doing that? an example is the set (1,1,1),(0,1,0),(1,2,3)
Reducing that; I get
also the identity matrix.
What i don't understand is how to find the span of the vector above (1,1,1),(0,1,0),(1,2,3)
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The span is the set of all linear combinations of (1,1,1),(0,1,0),and (1,2,3).
So S=a(1,1,1)+b(0,1,0)+c(1,2,3).
It forms a span because none of the vectors is a linear combination of the other two vectors.
So each vector can take the form,
a(1,1,1)+b(0,1,0)+c(1,2,3)=(1,3,2)
which leads to the matrix equation,

which leads to

.
.
Similarly for (0,1,0),

and for (1,2,3),

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