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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?

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?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 7CR
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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?
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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