(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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Question

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?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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