Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer. T(X1.X2.X3) = (X1 - 5x2 + 5X3, X2 = 9X3) (a) Is the linear transformation one-to-one? O A. Tis not one-to-one because the columns of the standard matrix A are linearly independent. O B. Tis one-to-one because T(x) = 0 has only the trivial solution. O C. Tis not one-to-one because the columns of the standard matrix A are linearly dependent. O D. Tis one-to-one because the column vectors are not scalar multiples of each other. (b) Is the linear transformation onto? O A. Tis not onto because the columns of the standard matrix A span R2. B. Tis onto because the standard matrix A does not have a pivot position for every row. С. Tis onto because the columns of the standard matrix A span R. O D. Tis not onto because the standard matrix A does not have a pivot position for every row.
Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer. T(X1.X2.X3) = (X1 - 5x2 + 5X3, X2 = 9X3) (a) Is the linear transformation one-to-one? O A. Tis not one-to-one because the columns of the standard matrix A are linearly independent. O B. Tis one-to-one because T(x) = 0 has only the trivial solution. O C. Tis not one-to-one because the columns of the standard matrix A are linearly dependent. O D. Tis one-to-one because the column vectors are not scalar multiples of each other. (b) Is the linear transformation onto? O A. Tis not onto because the columns of the standard matrix A span R2. B. Tis onto because the standard matrix A does not have a pivot position for every row. С. Tis onto because the columns of the standard matrix A span R. O D. Tis not onto because the standard matrix A does not have a pivot position for every row.
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:Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer.
T(X1,X2 .X3) = (x1 - 5x2 + 5×3, X2 - 9x3)
...
(a) Is the linear transformation one-to-one?
A. Tis not one-to-one because the columns of the standard matrix A are linearly independent.
B. Tis one-to-one because T(x) = 0 has only the trivial solution.
O C. Tis not one-to-one because the columns of the standard matrix A are linearly dependent.
O D. Tis one-to-one because the column vectors are not scalar multiples of each other.
(b) Is the linear transformation onto?
O A. Tis not onto because the columns of the standard matrix A
R2.
span
O B. Tis onto because the standard matrix A does not have a pivot position for every row.
O C. Tis onto because the columns of the standard matrix A span R2.
D. Tis not onto because the standard matrix A does not have a pivot position for every row.
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