(a)Let A be a 4×4 matrix and ~b, ~c be vectors in R4. Suppose A~x=~b has a unique solution. What can you say about the number of solutions of the system A~x=~c? (b) Let B be a 4×4 matrix and ~b, ~c be vectors in R4. Suppose B~x=~b is inconsistent. What can you say about the number of solutions of the system B~x=~c? (c) Let Cbe a 4×3 matrix and ~b, ~c be vectors in R4. Suppose C~x=~b has a unique solution. What can you say about the number of solutions of the system C~x=~c?
(a)Let A be a 4×4 matrix and ~b, ~c be vectors in R4. Suppose A~x=~b has a unique solution. What can you say about the number of solutions of the system A~x=~c? (b) Let B be a 4×4 matrix and ~b, ~c be vectors in R4. Suppose B~x=~b is inconsistent. What can you say about the number of solutions of the system B~x=~c? (c) Let Cbe a 4×3 matrix and ~b, ~c be vectors in R4. Suppose C~x=~b has a unique solution. What can you say about the number of solutions of the system C~x=~c?
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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7. (a)Let A be a 4×4 matrix and ~b, ~c be vectors in R4. Suppose A~x=~b has a unique solution. What can you say about the number of solutions of the system A~x=~c?
(b) Let B be a 4×4 matrix and ~b, ~c be vectors in R4. Suppose B~x=~b is inconsistent. What can you say about the number of solutions of the system B~x=~c?
(c) Let Cbe a 4×3 matrix and ~b, ~c be vectors in R4. Suppose C~x=~b has a unique solution. What can you say about the number of solutions of the system C~x=~c?
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