dot product of a matrix
must have (m n) (n y)multiply row by column
The dot product of two matrices, also known as the matrix product, is a binary operation in which we take the product of rows from one matrix with columns from the other matrix.
Given two matrices A and B, with dimensions of n×m and m×p respectively, the dot product AB results in a n×p matrix. Let’s see how it works.
Suppose we have two matrices:
A = [a1, a2, a3] where
a1 = [2, 3, 4],
a2 = [1, 0, -1],
a3 = [5, 2, 6]
and
B = [b1, b2, b3, b4] where
b1 = [4],
b2 = [-1],
b3 = [3].
b4 = [0]
To calculate the matrix product AB, we take the dot product of each row of A with each column of B, as follows:
AB = [a1b1 + a2b2 + a3b3, a1b4 + a2b5 + a3b6]
= [(2*4)+(3*-1)+(4*3), (2*0)+(3*0)+(4*0), (2*4)+(3*-1)+(4*3)]
[5 , 0, 17]
Therefore, the result of the dot product of matrices A and B is a 3×1 matrix:
AB = [5, 0, 17]
More Answers:
Mastering Calculus: Finding Instantaneous Rate Of Change Using DerivativesAverage Rate Of Change: Definition, Formula, And Real-World Applications
Using The Intermediate Value Theorem To Prove Solutions In Calculus: A Comprehensive Guide