00:01
Okay, so we're giving these two matrices, matrix a and matrix b.
00:04
So the column vectors of matrix a, while those would be c1 is equal to the column vector 14, and c2 is equal to the column vector 25, and c3 is equal to the column vector 36.
00:28
Okay, and then the row vectors of matrix b, those would be.
00:33
R1 is equal to the majoring vector 1 -2 and then r2 is equal to the row vector 3 -4 and r3 is equal to the row vector 5 -6.
00:52
So now the column row expansion of ab can be written as ab is equal to well c1 times r1 so we get the column vector 1, 4 times the row vector 1, 2, and then plus the column vector 25 times the row vector 3 ,4, and then plus the column vector 3 ,6, times the row vector 5, 6.
01:39
Okay, so, well, we look at, so we have, again, the first matrix here is going to be a a two by one, right, two rows, one column, and the row vector is going to be a one row, two columns, one by two.
01:56
That's the same in every case here, right? so yes, multiplication is defined because the inner numbers match up, the number of rows, or number of columns, excuse me, the first matrix is equal to the number of rows of the second matrix.
02:11
So then, yes, we can go ahead and multiply, and what we get would be the outer numbers here.
02:16
We get a two by two.
02:17
Matrix...