Let A be a 5 × 7 matrix, B be a 7 × 2 matrix, and C be a 2 × 3 matrix. (a) What
ID: 3796484 • Letter: L
Question
Let A be a 5 × 7 matrix, B be a 7 × 2 matrix, and C be a 2 × 3 matrix.
(a) What is the size of ABC?
(b) How many operations (additions plus multiplications) does it take to compute AB?
(c) How many operations (additions plus multiplications) does it take to compute BC?
(d) How many operations (additions plus multiplications) does it take to compute ABC by first computing AB and then multiplying the result by C?
(e) How many operations (additions plus multiplications) does it take to compute ABC by first computing BC and then multiplying the result by A?
Explanation / Answer
a)
A*B will have size 5 x 2 .
A*B*C will have size 5 x 3 .
b)
if we are multiplying [n x m] matrix to a [m x p] matrix then the number of operations will be:
m*n*p multiplications and np additions
A = [5 x 7]
B = [7 x 2]
no. of multiplications: 7*5*2=70
np. of additions : 5*2=10
total = 80
c)
B=[7 x 2]
C=[2 x 3]
addition: 7*3=21
multiplication : 7*2*3=42
total = 63
d)
AB =[5 x 2]
C = [2 x 3]
number of opeartion to compute AB is 80. (from (b))
to compute ABC the number of operations:
addition:5*3=15
multiplication : 5*3*2=30
total operation = 45+80=125
e)
A = [5 x 7]
BC=[7 x 3]
to compute ABC no. of operations:
multiplication : 5*7*3= 105
addition : 15
total= 70+15+no of operations for BC=120+63=183
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