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.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 41E

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