Matrices
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Let B, C, D, E, F and G be the following matrices:
1 3
2 6
3 9
1 -1 0
0 2 3
0 0 2
1 -1 0
0 1 1
1 0 1
2 1 0 0
0 0 -1 -1
0 0 0 3
0 0 0 0
1 1
3 4
4 6
-2 -3
I would welcome an explanation of whether:
- the columns of each matrix are independent
- the rows of each matrix are independent
- the columns of each matrix span R2 or R3
- the rows of each matrix span R3
- the rank of each matrix is 1 or 2.
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[1]
the second and third rows are multiples of the first; so the rows aren't independent, and neither are the columns.
the rows span a 1-dimensional subspace of R^2, and the columns span a 1-dimensional subspace of R^3
the row rank = column rank = 1 in this case ...
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