# 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.

https://brainmass.com/math/matrices/matrices-144516

#### Solution Preview

[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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