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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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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...
Number of Scalar Multiplications in Matrix Multiplication:
In matrix multiplication, the number of scalar multiplications required depends on the dimensions of the matrices involved. Let's analyze the given matrices M1, M2, M3, and M4 and calculate the number of scalar multiplications required for different multiplication orders.
Given:
p = 10
q = 100
r = 20
s = 5
t = 80
1. ((M1 X M2) X (M3 X M4)):
In this case, we first multiply M1 and M2, resulting in a matrix of dimension pxr. Then, we multiply M3 and M4, resulting in a matrix of dimension rxs. Finally, we multiply the two resulting matrices.
- M1 X M2:
- Number of scalar multiplications = p*q*r = 10*100*20 = 20,000
- M3 X M4:
- Number of scalar multiplications = r*s*t = 20*5*80 = 8,000
- ((M1 X M2) X (M3 X M4)):
- Number of scalar multiplications = (p*r*s) + (p*r*t) = (10*20*5) + (10*20*80) = 1,000 + 16,000 = 17,000
2. (((M1 X M2) X M3) X M4):
In this case, we first multiply M1 and M2, resulting in a matrix of dimension pxr. Then, we multiply the resulting matrix with M3, resulting in a matrix of dimension pxs. Finally, we multiply the resulting matrix with M4.
- M1 X M2:
- Number of scalar multiplications = p*q*r = 10*100*20 = 20,000
- (M1 X M2) X M3:
- Number of scalar multiplications = (p*r*q) + (p*s*r) = (10*20*100) + (10*5*20) = 20,000 + 1,000 = 21,000
- ((M1 X M2) X M3) X M4:
- Number of scalar multiplications = (p*s*t) + (p*r*t) = (10*5*80) + (10*20*80) = 4,000 + 16,000 = 20,000
Therefore, the total number of scalar multiplications required when multiplied as ((M1 X M2) X (M3 X M4)) is 17,000, and the total number of scalar multiplications required when multiplied as (((M1 X M2) X M3) X M4) is 20,000.
Hence, the correct answer is option 'C' (19,000 scalar multiplications).
In matrix multiplication, the number of scalar multiplications required depends on the dimensions of the matrices involved. Let's analyze the given matrices M1, M2, M3, and M4 and calculate the number of scalar multiplications required for different multiplication orders.
Given:
p = 10
q = 100
r = 20
s = 5
t = 80
1. ((M1 X M2) X (M3 X M4)):
In this case, we first multiply M1 and M2, resulting in a matrix of dimension pxr. Then, we multiply M3 and M4, resulting in a matrix of dimension rxs. Finally, we multiply the two resulting matrices.
- M1 X M2:
- Number of scalar multiplications = p*q*r = 10*100*20 = 20,000
- M3 X M4:
- Number of scalar multiplications = r*s*t = 20*5*80 = 8,000
- ((M1 X M2) X (M3 X M4)):
- Number of scalar multiplications = (p*r*s) + (p*r*t) = (10*20*5) + (10*20*80) = 1,000 + 16,000 = 17,000
2. (((M1 X M2) X M3) X M4):
In this case, we first multiply M1 and M2, resulting in a matrix of dimension pxr. Then, we multiply the resulting matrix with M3, resulting in a matrix of dimension pxs. Finally, we multiply the resulting matrix with M4.
- M1 X M2:
- Number of scalar multiplications = p*q*r = 10*100*20 = 20,000
- (M1 X M2) X M3:
- Number of scalar multiplications = (p*r*q) + (p*s*r) = (10*20*100) + (10*5*20) = 20,000 + 1,000 = 21,000
- ((M1 X M2) X M3) X M4:
- Number of scalar multiplications = (p*s*t) + (p*r*t) = (10*5*80) + (10*20*80) = 4,000 + 16,000 = 20,000
Therefore, the total number of scalar multiplications required when multiplied as ((M1 X M2) X (M3 X M4)) is 17,000, and the total number of scalar multiplications required when multiplied as (((M1 X M2) X M3) X M4) is 20,000.
Hence, the correct answer is option 'C' (19,000 scalar multiplications).
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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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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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
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