Suppose that c¹, c² are both 3 × 1 matrices. Let A = [c¹c²] be augmented matrix with c¹ and c² and c³ as its columns. Answer the following (each answer should be a short sentence or two.) a.) What are the dimensions of A? (That is, how many rows and columns does it have?) b.) Does the equation Ax = b always have to have a solution? c.) Based on your answer to the last part, does (c¹, c²) have to include every 3 × 1 matrix? d.) Can the equation Ar = 0 have multiple solutions? e.) Based on your answer to the last part, do the vectors {c¹, (²) have to be linearly inde- pendent?
Suppose that c¹, c² are both 3 × 1 matrices. Let A = [c¹c²] be augmented matrix with c¹ and c² and c³ as its columns. Answer the following (each answer should be a short sentence or two.) a.) What are the dimensions of A? (That is, how many rows and columns does it have?) b.) Does the equation Ax = b always have to have a solution? c.) Based on your answer to the last part, does (c¹, c²) have to include every 3 × 1 matrix? d.) Can the equation Ar = 0 have multiple solutions? e.) Based on your answer to the last part, do the vectors {c¹, (²) have to be linearly inde- pendent?
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 that c¹, c² are both 3 × 1 matrices. Let A = [c¹c²] be augmented matrix
with c¹ and c² and c³ as its columns. Answer the following (each answer should be a short
sentence or two.)
a.) What are the dimensions of A? (That is, how many rows and columns does it have?)
b.) Does the equation Ax = b always have to have a solution?
c.) Based on your answer to the last part, does (c¹, c²) have to include every 3 × 1 matrix?
d.) Can the equation Ar = 0 have multiple solutions?
e.) Based on your answer to the last part, do the vectors {c¹, (²) have to be linearly inde-
pendent?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34cc5c6b-5450-4c98-93f3-d37eba173724%2F4f467b2f-b988-4de5-83ca-fb5efe2ff1f1%2F7sxy9kl_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that c¹, c² are both 3 × 1 matrices. Let A = [c¹c²] be augmented matrix
with c¹ and c² and c³ as its columns. Answer the following (each answer should be a short
sentence or two.)
a.) What are the dimensions of A? (That is, how many rows and columns does it have?)
b.) Does the equation Ax = b always have to have a solution?
c.) Based on your answer to the last part, does (c¹, c²) have to include every 3 × 1 matrix?
d.) Can the equation Ar = 0 have multiple solutions?
e.) Based on your answer to the last part, do the vectors {c¹, (²) have to be linearly inde-
pendent?
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