Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer_ T(x1,x2x3) = (x₁ - 6x₂ + 4x3, x₂ − 7×3) (a) Is the linear transformation one-to-one? www. OA. T is one-to-one because T(x) = 0 has only the trivial solution. OB. T is one-to-one because the column vectors are not scalar multiples of each other. O C. T is not one-to-one because the columns the standard matrix A are linearly independent. OD. T is not one-to-one because the columns of the standard matrix A are linearly dependent. (b) Is the linear transformation onto? OA. T is not onto because the columns of the standard matrix A span R² OB. T is onto because the columns of the standard matrix A span OC. T is onto because the standard matrix A does not have a pivot position for every row. OD. T is not onto because the standard matrix A does not have a pivot position for every row. 2
Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer_ T(x1,x2x3) = (x₁ - 6x₂ + 4x3, x₂ − 7×3) (a) Is the linear transformation one-to-one? www. OA. T is one-to-one because T(x) = 0 has only the trivial solution. OB. T is one-to-one because the column vectors are not scalar multiples of each other. O C. T is not one-to-one because the columns the standard matrix A are linearly independent. OD. T is not one-to-one because the columns of the standard matrix A are linearly dependent. (b) Is the linear transformation onto? OA. T is not onto because the columns of the standard matrix A span R² OB. T is onto because the columns of the standard matrix A span OC. T is onto because the standard matrix A does not have a pivot position for every row. OD. T is not onto because the standard matrix A does not have a pivot position for every row. 2
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 - 6x2 + 4x3, X2 - 7x3)
(a) Is the linear transformation one-to-one??
OD
OA. T is one-to-one because T(x) = 0 has only the trivial solution.
OB. T is one-to-one because the column vectors are not scalar multiples of each other.
O C. T is not one-to-one because the columns the standard matrix A are linearly independent.
OD. T is not one-to-one because the columns of the standard matrix A are linearly dependent.
(b) Is the linear transformation onto?
OA. T is not onto because the columns of the standard matrix A span R²
OB. T is onto because the columns of the standard matrix A span R².
O C. T is onto because the standard matrix A does not have a pivot position for every row.
OD. T is not onto because the standard matrix A does not have a pivot position for every row.
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