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Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(X1,X2.X3,X4) = (X2 + X3,X2 + X3,X3 + X4,0) a. Is the linear transformation one-to-one? O A. Tis one-to-one because T(x) = 0 has only the trivial solution. B. Tis not one-to-one because the standard matrix A has a free variable. Oc. Tis not one-to-one because the columns of the standard matrix A are linearly independent. 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 R4. O B. Tis onto because the columns of the standard matrix A span R4. OC. Tis not onto because the fourth row of the standard matrix A is all zeros. O D. Tis 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 your answer. T(X1,X2.X3,X4) = (X2 + X3,X2 + X3,X3 + X4,0) a. Is the linear transformation one-to-one? O A. Tis one-to-one because T(x) = 0 has only the trivial solution. B. Tis not one-to-one because the standard matrix A has a free variable. Oc. Tis not one-to-one because the columns of the standard matrix A are linearly independent. 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 R4. O B. Tis onto because the columns of the standard matrix A span R4. OC. Tis not onto because the fourth row of the standard matrix A is all zeros. O D. Tis onto because the standard matrix A does not have a pivot position for every row.

Elementary Linear Algebra (MindTap Course List)
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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Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(X1,X2,X3,X4) = (X2 + X3,X2 + X3.X3 + X4,0) a. Is the linear transformation one-to-one? O A. Tis one-to-one because T(x) = 0 has only the trivial solution. O B. Tis not one-to-one because the standard matrix A has a free variable. O c. Tis not one-to-one because the columns of the standard matrix A are linearly independent. 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 R4. B. Tis onto because the columns of the standard matrix A span R4. OC. Tis not onto because the fourth row of the standard matrix A is all zeros. O D. Tis onto because the standard matrix A does not have a pivot position for every row.
Transcribed Image Text:Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(X1,X2,X3,X4) = (X2 + X3,X2 + X3.X3 + X4,0) a. Is the linear transformation one-to-one? O A. Tis one-to-one because T(x) = 0 has only the trivial solution. O B. Tis not one-to-one because the standard matrix A has a free variable. O c. Tis not one-to-one because the columns of the standard matrix A are linearly independent. 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 R4. B. Tis onto because the columns of the standard matrix A span R4. OC. Tis not onto because the fourth row of the standard matrix A is all zeros. O D. Tis onto because the standard matrix A does not have a pivot position for every row.
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