Disclaimer: this is not for homework, rather a request for clarification of a rather basic concept
In my linear algebra book, it states at the columns of AB (A and B are matrices) are just combinations of the columns of A. How? I know there are multiple ways of visualizing matrix multiplication but I’m just not seeing this one.
I’ve always only been able to multiply matrices by going across the row of the left matrix and multiplying by the same column of the second. This isn’t helpful in visualizing the columns, though.
For example, I get the following perfectly:
| 8 2 8 | A=| 2 1 1 | | 4 2 7 | | x1 | B=| x2 | | x3 | |8| |2| |8| AB = x1*|2| + x2*|1| + x3*|1| |4| |2| |7|
I think it’s just when B is more than a column vector, I get confused. And quickly.
It also says that the columns of AB are simply matrix A times the columns of B. Why doesn’t that mean that the columns of AB are combinations of the columns of B?
The book also states there’s a column-row picture for matrix multiplication in that the columns of A are multiplied by the rows of B, but it states no more and gives no examples. Help? I’m an engineering student and this abstract material is killing me. :smack: