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Consider three matrices A (10 × 100), B (100 × 5), C (5 × 50). What is total number of multiplications required?

Your Answer:

500

Correct Answer: 7500    Status: incorrect

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Matrix multiplication:

A is pxq and B is qxr C is rxs then  no of mul's required for AB=p*q*r and order of AB is pxr.

(AB) is pxr and C is rxs no of mul's required for (AB)C=pxs.

Total no of multiplications needed=#mul's(AB)+#((AB)C)=p*q*r+p*r*s

ABC is done in two ways I)(AB)C and II) A(BC)

Case I) (AB)C

No of multiplications for AB=10*100*5=5000 and order of AB is 10x5

(AB)C no of multiplications=10*5*50=2500.

Total no of multiplications=5000+2500=${\color{Red} 7500}$

Case II) A(BC)

No of multiplications for BC=100*5*50=25000 and order of BC is 100x5

A(BC) no of multiplications=10*100*5=5000

Total no of multiplications=25000+5000=30000

Consider less no of multiplications i.e)  7500

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