Linear Algebra help!

[oreo]

Have a test review and there are a few questions that I have no idea what the answer could be:

Give two row-equivalent matrices A and B such that the column space of A and the column space of B are not equal.
Find a matrix A such that the Null space of A has basis
|1|
|2|


I know how to get the null space of a matrix but have no clue how you would work backwards. Any help would be much appreciated.

[Streetwolf]

#1:

A and B are both 2x2 written as: (a11 a12 // a21 a22)

A = (1 2 // 3 4)
B = (3 4 // 1 2)

#2:

A = (2, -1)

Since the basis is (1, 2) you have 2x1 = x2 ==> 2x1 - x2 = 0 so your matrix can be (2, -1). When you multiply (2, -1) * (1, 2) you get (0). Any matrix (2, -1) * a scalar lambda will be an answer.

[oreo]

i love you, thanks