Find the matrix product, if possible:
[6 0 -4 ] ]1]
[1 2 5 ] [2]
[10 -1 3 ] [0]
Matrix products are defined if they are compatible in size.
Am,n is a matrix of m rows and n columns, and a vector B of n elements can be considered as a matrix Bn,1.
Specifically, the matrix product between A and B is defined when the number of columns of A equals the number of rows of B, or
Cm,p = Am,n Bn,p.
In the given case, we have
Am,n=A3,3
and
Bn,p=B3,1
So the matrix product is defined as
C3,1 = AB
The element ci,j of the product matrix C is defined as the inner product (dot product) of row i of A and column j of B.
In the given example, c2,1 is calculated as the dot product of the second row of A [1 2 5] and the first column of B [1 2 0] which gives
c2,1
=[1 2 5].[1 2 0]
=1*1+2*2+5*0
=5
Continue this way for all the elements of C and you'll have the matrix product.
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