Hey guys, I understand matrices and their tranpose but I have this question which is just confusing... maybe it's because it's late but anyway it reads:
Given the two vectors: A = [1, 2] B = [3, 4] calculate:
A B^{T} and B A^{T}
So I did this
A = [1, 2]
B =
[3]
[4]
But I don't get what to do next... I can't multiple these can I?
P.S I really must learn how to insert the proper mathematical code to format my questions correctly
Nevermind I just worked it out. I was checking my results using a website that has a calculator for matraces. But it only went from 2x2 - 1x3 - 3x3 so I just assumed 1x2 and 1x1 did not exist...
So I got this as my answer
AB^{T }I got 11
BA^{T} I got 11
A^{T}B I got 11
B^{T}A I got 11
Which were the four questions I had to work out so for a conclusion I just wrote, not matter which way you switch them around you'll always get the same answer?
If you multiply two matrices and , each entry of the resulting product is found by multiplying (taking the dot product of) the row of by the column of .
We have a 2x1 matrix times a 1x2 matrix, so we should expect our answer to be 2x2:
.
So, using the above definition of matrix multiplication, is given by the dot product of the first row of and the first column of : . And so on.
Since the rows of and the columns of have only one entry each, there is no addition to be done.