Can each vector in R* be written as a linear combination of the columns of the matrix A? Do the columns of A span R*? 2 4 -5 10 -1 -1 1 0 A = - 4 0 - 2 20 2 -3 13 Can each vector in R* be written as a linear combination of the columns of the matrix A? Select the correct choice below and fill in the answer box to complete your choice (Type an integer or decimal for each matrix element.) O A. Yes, because the reduced echelon form of A is O B. No, because the reduced echelon form of A is Do the columns of A span R*? O A. No, because A has a pivot position in every row. O B. Yes, because A does not have a pivot position in every row. O C. Yes, because all b in R" can be written as a linear combination of the columns of A. O D. No, because not all b in R" can be written as a linear combination of the columns of A.
Can each vector in R* be written as a linear combination of the columns of the matrix A? Do the columns of A span R*? 2 4 -5 10 -1 -1 1 0 A = - 4 0 - 2 20 2 -3 13 Can each vector in R* be written as a linear combination of the columns of the matrix A? Select the correct choice below and fill in the answer box to complete your choice (Type an integer or decimal for each matrix element.) O A. Yes, because the reduced echelon form of A is O B. No, because the reduced echelon form of A is Do the columns of A span R*? O A. No, because A has a pivot position in every row. O B. Yes, because A does not have a pivot position in every row. O C. Yes, because all b in R" can be written as a linear combination of the columns of A. O D. No, because not all b in R" can be written as a linear combination of the columns of A.
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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Transcribed Image Text:Can each vector in R* be written as a linear combination of the columns of the matrix A? Do the columns of A span R*?
2
4 -5 10
-1 -1
1 0
A =
- 4
0 - 2 20
2 -3 13
Can each vector in R* be written as a linear combination of the columns of the matrix A? Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or decimal for each matrix element.)
O A. Yes, because the reduced echelon form of A is
O B. No, because the reduced echelon form of A is
Do the columns of A span R4?
O A. No, because A has a pivot position in every row.
O B. Yes, because A does not have a pivot position in every row.
O C. Yes, because all b in R" can be written as a linear combination of the columns of A.
D. No, because not all b in R" can be written as a linear combination of the columns of A.
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