Thread: linear combination of rows

Let a be a 1 x n matrix and B an n x p matrix. Show that the matrix product aB can be written as a linear combination of rows of B where the coefficients are the entries of A.

I don't get how you can have a combination of rows.

Linear combination of rows just means treating each row as a vector, and the final resulting product aB is a vector which is some linear combination of all the row vectors.

Hint: Notice that during multiplication, each element on the same row is multiplied by the same factor before being added.

aB = [1(2)+-2(-2)+3(4) 1(1)+-2(-2)+3(5) 1(-4)+-2(3)+3(-2)]
I see how the rows are inside the elements but how do I write this as an linear combination?

Write:



Then,




Fernando Revilla