matrix multiplication

Question

consider  3  matrices

A[100*200]

B[200*50]]

C[50*30]

Suppose a computer  takes

1) 1 microsecond to multiply 2  numbers.

2) almost 0 second to perform Addition.

 

Then  find out  how much time the computer  will  take  to  Multiply matrices in  All possible ways.

Assume  the Matrix multiplication procedure to be continuous  without any   time delay.

options are--

1) 0.5 seconds

2) 1.5 seconds

3) 2 seconds

4) 3 seconds

Comments

m getting 0.63
if go with options then b will be answer i.e. 1.15 sec. but that is worst idea.

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total no. multiplications required = 100*200*50 + 100*50*30 = 1000000+150000=1150000/1microsec = 1.15 sec

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not per microsecong it will be in multiply

Answer 1

There are three ways two multiply 3 Matrices

((AB)C)  and (A(BC))

Total number of multiplication in ((AB)C)

Multiplication in AB=100*200*50 =1000,000 

Let AB=D

Multiplication in DC=100*50*30 =150,000

So, Total number of multiplication in ((AB)C) = 1000,000+150,000 = 1150,000 

it Takes 1.15  second

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Total number of multiplication in (A(BC))

Multiplication in BC=200*50*30 = 300,000

let BC=D

Multiplication in AD=100*200*30 =600,000

So, Total number of multiplication in (A(BC))=300,000 + 600,000 == 900,000

it Takes 0.9 second

So,total Time is1.15+ 0.9=2.05 second

Comments

total time is 0.9 right? how you got 2.05?

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There are two ways to multiply 3 Matrices

((AB)C) =1.15 and

(A(BC))=0.9

total=1.15+0.9=2.05

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find out  how much time the computer  will  take  to  Multiply matrices in  All possible ways

this doesn't means we need to add the time

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So, we should take the best among all possible,  right?

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yeah that's what i'm saying

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In the question it says $"$ find out  how much time the computer  will  take  to  Multiply matrices in  All possible ways $".$

So we can add all cases and get the answer.