Do the columns of A span R4? Does the equation Ax = b have a solution for each b in R¹? 1 4 -1 -5 0 2 2-4 A = 2 3 -7 0 -3-9 6 12 Do the columns of A span R4? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) A. Yes, because the reduced echelon form of A is 10-50 01 10 B. No, because the reduced echelon form of A is 0 0 0 1 0 0 0 0 Does the equation Ax = b have a solution for each bin R4? OA. No, because the columns of A do not span R4. OB. Yes, because A does not have a pivot position in every row. OC. Yes, because the columns of A span R4. OD. No, because A has a pivot position in every row.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 42EQ
Question

Please solve part B

Do the columns of A span R4? Does the equation Ax = b have a solution for each b in R¹?
1
4 -1 -5
0
2 2-4
A =
2
3 -7 0
-3-9 6 12
Do the columns of A span R4? Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or decimal for each matrix element.)
A. Yes, because the reduced echelon form of A is
10-50
01
10
B. No, because the reduced echelon form of A is
0 0
0 1
0 0
0 0
Does the equation Ax = b have a solution for each bin R4?
OA. No, because the columns of A do not span R4.
OB. Yes, because A does not have a pivot position in every row.
OC. Yes, because the columns of A span R4.
OD. No, because A has a pivot position in every row.
Transcribed Image Text:Do the columns of A span R4? Does the equation Ax = b have a solution for each b in R¹? 1 4 -1 -5 0 2 2-4 A = 2 3 -7 0 -3-9 6 12 Do the columns of A span R4? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) A. Yes, because the reduced echelon form of A is 10-50 01 10 B. No, because the reduced echelon form of A is 0 0 0 1 0 0 0 0 Does the equation Ax = b have a solution for each bin R4? OA. No, because the columns of A do not span R4. OB. Yes, because A does not have a pivot position in every row. OC. Yes, because the columns of A span R4. OD. No, because A has a pivot position in every row.
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