Time for action - doing multiplication operations

Let us try to perform some of the same operations for multiplication as we did for addition:

octave:75> a*a
ans = 4
octave:76> a*b
ans =
2 4 6
octave:77> b*b
error: operator *: nonconformant arguments (op1 is 1x3, op2 is 1x3)
octave:78> b*c
ans = 14

What just happened?

From Command 75, we see that * multiplies two scalar variables just like standard multiplication. In agreement with linear algebra, we can also multiply a scalar by each element in a vector as shown by the output from Command 76. Command 77 produces an error—recall that b is a row vector which Octave also interprets as a 1 x 3 matrix, so we try to perform the matrix multiplication (1 x 3)(1 x 3), which is not valid. In Command 78, on the other hand, we have (1 x 3)(3 x 1) since c is a column vector yielding a matrix with size 1 x 1, that is, a scalar. This is, of course, just the dot product between b and c.

Let us try an additional example and perform the matrix...