How does one multiply a row vector by a matrix?

Question

say you have C=(0 1 0 0), and A =
0 0 1 0
0 0 0 1
-1 1 0 0
1 -2 0 0

how do you get an outcome?

do you do c_1 * a_11 + c_2 * a_12 + c_3 * a_13 + c_4 * a_14, etc.? or something else? (underscore meant to denote subscripts).

Answer 1

What you wrote would be the result of multiplying A*C^T, where C^T is the COLUMN vector C-transpose. For C*A you want c_1*a_11 + c_2*a_21 + c_3*a_31 + c_4*a_41. Notice that C*A is a 1X4 matrix, while A*C^T is 4X1.