# Linear Algebra - Concept Question

1. Nov 18, 2013

### ChemistryNat

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Since matrix B is an invertible 2x2 matrix, its row reduced echelon form will be the 2x2 identity matrix. Therefore, B, has rowspace span{[1,0][0,1]}, nullspace is the empty set and dimcol(B) is 2

Row reducing the given numerical matrix gives [(1,0),(0,1),(0,0)]
which has rowspace span{[1,0][0,1]}, nullspace is the empty set and columnspace span {[2,-1,0],[2,3,1]}

Since the nullspace and rowspace of matrix B and the numerical matrix are equal, is this sufficient to say that the product, matrix A will also have the same nullspace and rowspace?

Since the numerical matrix is a 3x2 and B is 2x2, then A is 3x2
so the columnspace of A must involve column vectors with 3 variables
I'm assuming that the columns of A are linearly dependent on the columns of that explicit matrix and that the columns of A are the columns of the explicit matrix?

thank you!

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