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How many rows of A contain a pivot position? Does the equation Ax = b have a solution for each b in R4? 2 4 -1 -2 -2 -2 A = - 4 6 - 12 5 - 10 How many rows of A contain a pivot position? A has rows which contain a pivot position. Does the equation Ax = b have a solution for each b in R“? А. Yes, because the reduced echelon form of A does not have a row of the formo ... 0 b with b nonzero. В. No, because each b in R4 is a linear combination of the columns of A. O C. Yes, because the columns of A do not span R*. D. No, because A does not have a pivot position in every row.

How many rows of A contain a pivot position? Does the equation Ax = b have a solution for each b in R4? 2 4 -1 -2 -2 -2 A = - 4 6 - 12 5 - 10 How many rows of A contain a pivot position? A has rows which contain a pivot position. Does the equation Ax = b have a solution for each b in R“? А. Yes, because the reduced echelon form of A does not have a row of the formo ... 0 b with b nonzero. В. No, because each b in R4 is a linear combination of the columns of A. O C. Yes, because the columns of A do not span R*. D. No, because A does not have a pivot position in every row.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 4CEXP
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How many rows of A contain a pivot position? Does the equation Ax = b have a solution for each b in R*? 2 4 - 1 6. -2 -2 - 2 A = - 4 - 12 2 5 - 10 How many rows of A contain a pivot position? has rows which contain a pivot position. Does the equation Ax = b have a solution for each b in R*? O A. Yes, because the reduced echelon form of A does not have a row of the form 0 b with b nonzero. О В. No, because each b in R* is a linear combination of the columns of A. C. Yes, because the columns of A do not span R*. O D. No, because A does not have a pivot position in every row.
Transcribed Image Text:How many rows of A contain a pivot position? Does the equation Ax = b have a solution for each b in R*? 2 4 - 1 6. -2 -2 - 2 A = - 4 - 12 2 5 - 10 How many rows of A contain a pivot position? has rows which contain a pivot position. Does the equation Ax = b have a solution for each b in R*? O A. Yes, because the reduced echelon form of A does not have a row of the form 0 b with b nonzero. О В. No, because each b in R* is a linear combination of the columns of A. C. Yes, because the columns of A do not span R*. O D. No, because A does not have a pivot position in every row.
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