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Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed is
- a)248000
- b)44000
- c)19000
- d)25000
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt re...
It is basically matrix chain multiplication problem. We get minimum number of multiplications using ((M1 X (M2 X M3)) X M4). Total number of multiplications = 100x20x5 (for M2 x M3) + 10x100x5 + 10x5x80 = 19000.
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Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt re...
Solution:
Given, p = 10, q = 100, r = 20, s = 5 and t = 80.
We need to find the number of scalar multiplications needed for the matrices M1, M2, M3 and M4.
As per the question, we have two ways to multiply these matrices:
1. ((M1 X M2) X (M3 X M4))
2. (((M1 X M2) X M3) X M4)
Let's calculate the number of scalar multiplications required for both ways:
1. ((M1 X M2) X (M3 X M4))
Number of scalar multiplications required for M1 X M2 = p*q*r = 10*100*20 = 20000
Number of scalar multiplications required for M3 X M4 = r*s*t = 20*5*80 = 8000
Number of scalar multiplications required for ((M1 X M2) X (M3 X M4)) = p*q*r*s*t = 10*100*20*5*80 = 80000000
2. (((M1 X M2) X M3) X M4)
Number of scalar multiplications required for M1 X M2 = p*q*r = 10*100*20 = 20000
Number of scalar multiplications required for ((M1 X M2) X M3) = p*q*r*s = 10*100*20*5 = 100000
Number of scalar multiplications required for (((M1 X M2) X M3) X M4) = p*q*s*t = 10*100*5*80 = 400000
Therefore, the number of scalar multiplications needed for the matrices M1, M2, M3 and M4 is 19000 (option C).
Given, p = 10, q = 100, r = 20, s = 5 and t = 80.
We need to find the number of scalar multiplications needed for the matrices M1, M2, M3 and M4.
As per the question, we have two ways to multiply these matrices:
1. ((M1 X M2) X (M3 X M4))
2. (((M1 X M2) X M3) X M4)
Let's calculate the number of scalar multiplications required for both ways:
1. ((M1 X M2) X (M3 X M4))
Number of scalar multiplications required for M1 X M2 = p*q*r = 10*100*20 = 20000
Number of scalar multiplications required for M3 X M4 = r*s*t = 20*5*80 = 8000
Number of scalar multiplications required for ((M1 X M2) X (M3 X M4)) = p*q*r*s*t = 10*100*20*5*80 = 80000000
2. (((M1 X M2) X M3) X M4)
Number of scalar multiplications required for M1 X M2 = p*q*r = 10*100*20 = 20000
Number of scalar multiplications required for ((M1 X M2) X M3) = p*q*r*s = 10*100*20*5 = 100000
Number of scalar multiplications required for (((M1 X M2) X M3) X M4) = p*q*s*t = 10*100*5*80 = 400000
Therefore, the number of scalar multiplications needed for the matrices M1, M2, M3 and M4 is 19000 (option C).
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Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed isa)248000b)44000c)19000d)25000Correct answer is option 'C'. Can you explain this answer?
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Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed isa)248000b)44000c)19000d)25000Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed isa)248000b)44000c)19000d)25000Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed isa)248000b)44000c)19000d)25000Correct answer is option 'C'. Can you explain this answer?.
Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed isa)248000b)44000c)19000d)25000Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed isa)248000b)44000c)19000d)25000Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed isa)248000b)44000c)19000d)25000Correct answer is option 'C'. Can you explain this answer?.
Solutions for Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed isa)248000b)44000c)19000d)25000Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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