Let T be the linear transformation whose standard matrix is given. Decide whether T maps R5 onto R5. Justify your answer. Choose the correct answer below. A = 2 -7 3 -5 5 6-18 12 - 18 12 -6 12 -21 30-4 6-15 6-27 24-39 0 -3 3 16 OA. T maps R5 onto R5 because the equation Ax = 0 has free variables. B. T does not map R5 onto R5 because one of the columns of A is a linear combination of the other columns. O C. T does not map R5 onto R5 because the reduced echelon form of A does not have a pivot position in every row. OD. T maps R5 onto R5 because the reduced echelon form of A has a pivot position in every column.
Let T be the linear transformation whose standard matrix is given. Decide whether T maps R5 onto R5. Justify your answer. Choose the correct answer below. A = 2 -7 3 -5 5 6-18 12 - 18 12 -6 12 -21 30-4 6-15 6-27 24-39 0 -3 3 16 OA. T maps R5 onto R5 because the equation Ax = 0 has free variables. B. T does not map R5 onto R5 because one of the columns of A is a linear combination of the other columns. O C. T does not map R5 onto R5 because the reduced echelon form of A does not have a pivot position in every row. OD. T maps R5 onto R5 because the reduced echelon form of A has a pivot position in every column.
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:Let T be the linear transformation whose standard matrix is given.
Decide whether T maps R5 onto R5. Justify your answer.
Choose the correct answer below.
A=
2 -7
6-18
3 -5 5
12-18 12
-6 12 - 21
6 - 15
24
39 0
6-27
-3 3 16
30-4
O A. T maps R5 onto R5 because the equation Ax = 0 has free variables.
B.
T does not map R5 onto R5 because one of the columns of A is a linear combination of the
other columns.
O C.
T does not map R5 onto R5 because the reduced echelon form of A does not have a pivot
position in every row.
O D.
T maps R5 onto R5 because the reduced echelon form of A has a pivot position in every
column.
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