00:04
Okay, so today we will be covering problem 49 from chapter 4, section 4 of an algebra 2 textbook.
00:14
And our question is, we need to determine whether each matrix product is defined, and if so, state the dimensions of the product.
00:24
So the matrix product we're given is a, which is a 2x3 matrix, and b, which is a 3 by 2 matrix.
00:33
So before we can answer this question, we need to recall what the definition of a matrix product is.
00:43
So let a be an m by m by m matrix and be an m by p matrix.
00:47
Then the matrix product denoted ab, or as in the problem statement, a dot b.
00:55
So a b is the m by p matrix c, such that each entry c .i .j is the dot product of the i -th row of a and the jth column of b.
01:06
So here is a conceptualization of that...