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Suppose A is an n x n invertible unit lower triangular matrix and n » 10. A programmer claims that as solving a linear system Ax = b takes around 10 seconds, solving ten linear systems Ax; = b; for j = 1, ..., 10 will take around 100 seconds. Justify or refute this claim. FALSE. Just need to compute the LU factorization of the matrix A once, then use forward and back substitutions to solve LUx; = Pb, for j = 1, ..., 10. This will not take much more than 10 seconds. TRUE. It takes 10 times longer to compute the solution of 10 linear systems using just forward or back substitution.

Suppose A is an n x n invertible unit lower triangular matrix and n » 10. A programmer claims that as solving a linear system Ax = b takes around 10 seconds, solving ten linear systems Ax; = b; for j = 1, ..., 10 will take around 100 seconds. Justify or refute this claim. FALSE. Just need to compute the LU factorization of the matrix A once, then use forward and back substitutions to solve LUx; = Pb, for j = 1, ..., 10. This will not take much more than 10 seconds. TRUE. It takes 10 times longer to compute the solution of 10 linear systems using just forward or back substitution.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose A is an n x n invertible unit lower triangular matrix and n > 10. A programmer claims that as solving a linear system Aæ = b takes around 10 seconds, solving ten linear systems Aæ; = b; for j = 1, ..., 10 will take around 100 seconds. Justify or refute this claim. FALSE. Just need to compute the LU factorization of the matrix A once, then use forward and back substitutions to solve LUæ; = Pb; for j = 1, ..., 10. This will not take much more than 10 seconds. TRUE. It takes 10 times longer to compute the solution of 10 linear systems using just forward or back substitution.
Transcribed Image Text:Suppose A is an n x n invertible unit lower triangular matrix and n > 10. A programmer claims that as solving a linear system Aæ = b takes around 10 seconds, solving ten linear systems Aæ; = b; for j = 1, ..., 10 will take around 100 seconds. Justify or refute this claim. FALSE. Just need to compute the LU factorization of the matrix A once, then use forward and back substitutions to solve LUæ; = Pb; for j = 1, ..., 10. This will not take much more than 10 seconds. TRUE. It takes 10 times longer to compute the solution of 10 linear systems using just forward or back substitution.
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