Problem 3.1 #24 in the Strang Linear Algebra book, 4ed:
"The columns of AB are combinations of the columns of A. This means the column space of AB is contained in (possibly equal to) the column space of A. Give an example where the column spaces of A and AB are not equal."

I don't see that the column space of AB is contained in the column space of A. If A=
12
24

and B=
13
32

then AB equals
37
68

Here the col space of AB "has more" than the col space of A; in fact it contains the col space of A.
Did the book mean for B to be simply a vector and not a matrix?

Question

Problem 3.1 #24 in the Strang Linear Algebra book, 4ed:
"The columns of AB are combinations of the columns of A. This means the column space of AB is contained in (possibly equal to) the column space of A. Give an example where the column spaces of A and AB are not equal."

I don't see that the column space of AB is contained in the column space of A. If A=
12
24

and B=
13
32

then AB equals 
37
68

Here the col space of AB "has more" than the col space of A; in fact it contains the col space of A.
Did the book mean for B to be simply a vector and not a matrix?

anonymous · Answer

It looks like you've made a calculation error.  |dw:1351669669787:dw|

And, the column space of AB is the same as that of A, consisting of the line generated by the vector |dw:1351670203221:dw|

[Sorry about the lame brackets, I'm just learning about the drawing/equation tools]