Originally Posted by
PvtBillPilgrim I have this matrix made of two spanning sets:
1 1 3 2 0 8
5 4 14 3 1 9
-2 0 -4 -2 0 -8
3 3 9 0 1 3
In reduced row echelon form the matrix is:
1 0 2 0 1/6 0
0 1 1 0 1/6 0
0 0 0 1 -1/6 0
0 0 0 0 0 1
W1 is the span of the first three columns of the original matrix.
W2 is the span of the last three columns of the original matrix.
I need to find a basis for:
W1
W2
W1+W2
the intersection of W1 and W2
I think I'm wrong but I said that:
a basis for W1= {Column 1, Column 2}
a basis for W2={Column 4, Column 5}
a basis for W1+W2={Column 1, Column 2, Column 4, Column 6}
this means that there would be no basis for the intersection of W1 and W2
doesn't make sense
could someone check this?