8. An upper-triangular linear system has the form a11 0 0 0 a12 a13 a14 022 023 024 0 033 00 034 044 ZL I2 13 ZA b₁ b₂ b3 ba for example, in the case of a 4 x 4 system. Such systems are easily solved by back substitution (solve the last equation for 24, then the previous equation for 23, etc.) How many multiplication operations does this require? (Count a division the same as a multipli- cation, so computing 74=b4/a44 takes 1 "multiply", for example.) Exactly how many "multiplies" does it take to solve a general n x n upper-triangular system? In particular, how many to solve an upper-triangular system of 1000 equations?
8. An upper-triangular linear system has the form a11 0 0 0 a12 a13 a14 022 023 024 0 033 00 034 044 ZL I2 13 ZA b₁ b₂ b3 ba for example, in the case of a 4 x 4 system. Such systems are easily solved by back substitution (solve the last equation for 24, then the previous equation for 23, etc.) How many multiplication operations does this require? (Count a division the same as a multipli- cation, so computing 74=b4/a44 takes 1 "multiply", for example.) Exactly how many "multiplies" does it take to solve a general n x n upper-triangular system? In particular, how many to solve an upper-triangular system of 1000 equations?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 10E
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Transcribed Image Text:8. An upper-triangular linear system has the form
a12 a13 a14
022
023 a24
0
033 034
0
0
044
a11
0
0
0
21
X2
23
by
b₂
b3
ba
for example, in the case of a 4 x 4 system. Such systems are easily solved by back substitution
(solve the last equation for 24, then the previous equation for 23, etc.)
How many multiplication operations does this require? (Count a division the same as a multipli-
cation, so computing 74=b4/a44 takes 1 "multiply", for example.)
Exactly how many "multiplies" does it take to solve a general n x n upper-triangular system? In
particular, how many to solve an upper-triangular system of 1000 equations?
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