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Question from John, a student:

A=

1 1 0 0
1 1 0 0
0 0 1 0
0 0 1 1

B=

1 5 6
1 5 6
0 7 2
0 0 9

Is the space spanned by the columns of A the same as the space spanned by the columns of B?

John,

One way to approach this just from first principles is to ask if each of the three columns of B can be written as a linear combination of the columns of A. If so then the column space of B is a subset of the column space of A. In a similar way see if the column space of A is a subset of the column space of B.

Harley

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