Give an example of a matrix A such that (1) Ax = b has a solution for infinitely many b e R°, but (2) Ax = b does not have a solution for some b E R°. A =
Give an example of a matrix A such that (1) Ax = b has a solution for infinitely many b e R°, but (2) Ax = b does not have a solution for some b E R°. A =
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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Transcribed Image Text:b has a
Give an example of a matrix A such that (1) Ax
solution for infinitely many b E R°, but (2) Ax = b does
not have a solution for some b e R.
A =
Expert Solution
Step 1
If the dimension of the column space of A will be 3 (or if A has set of three linearly independent column.) then A span and we have infinitely many b.
And if the dimension of the column space of A will be less than 3 than A does not span and we get no solution for some b.
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