Question

I am stumped at lecture 2. In particular, Strang says that a matrix times a column yields a linear combination the columns. I've tried every thing I can think of, but all I get is a linear combination of the rows - which are the LHS of the original equations.

Similarly, he says that a row times a matrix yields linear combination of the rows. I keep on getting a linear combination of the columns.

Answer 1

Matrix times column yields combination of the columns of the matrix

2 4 x 1 = (2x1) + (4x1) = 6
1 3 1 (1x1) + (3x1) 4


Row times matrix yields combination of the rows of the matrix

1 1 x 2 4 = (1x2) + (1x1) (1x4) + (1x3) = 3 7
1 3

Answer 2

And keep in mind that addition is NOT commutative in matrix algebra so when he says a row times a matrix, that is exactly what he means.