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MMLU / To compute the matrix product M_1M_2, where M_1 has p rows and q columns and…

Problem

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question

To compute the matrix product M_1M_2, where M_1 has p rows and q columns and where M_2 has q rows and r columns, takes time proportional to pqr, and the result is a matrix of p rows and r columns. Consider the product of three matrices N_1N_2N_3 that have, respectively, w rows and x columns, x rows and y columns, and y rows and z columns. Under what condition will it take less time to compute the product as (N_1N_2)N_3 (i.e., multiply the first two matrices first) than to compute it as N_1(N_2 N_3)?

choices

  1. There is no such condition; i.e., they will always take the same time.
  2. 1/x + 1/z < 1/w + 1/y
  3. x > y
  4. 1/w + 1/x < 1/y + 1/z

subject

college_computer_science

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Source and history

task_id
d5502d3c-d009-525f-afa6-d32e09cf4dc4
task_key
all--test--d5502d3c-d009-525f-afa6-d32e09cf4dc4
task_revision_id
1
config / split
all / test

Official source

initial import