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Determine if the specified linear transform T(X₁ X2 X3 X4) = (x₁ + x₂,0₁X3 + X₁₁X_ a. Is the linear transformation one-to-one OA. T is one-to-one because the colum OB. T is one-to-one because T(x)=0 H OC. T is not one-to-one because the st OD. T is not one-to-one because the co b. Is the linear transformation onto? OA. T is onto because the columns of t OB. T is not onto because the second m OC. T is onto because the standard ma OD. T is not onto because the columns

Determine if the specified linear transform T(X₁ X2 X3 X4) = (x₁ + x₂,0₁X3 + X₁₁X_ a. Is the linear transformation one-to-one OA. T is one-to-one because the colum OB. T is one-to-one because T(x)=0 H OC. T is not one-to-one because the st OD. T is not one-to-one because the co b. Is the linear transformation onto? OA. T is onto because the columns of t OB. T is not onto because the second m OC. T is onto because the standard ma OD. T is not onto because the columns

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 26EQ
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Q25 Please provide justified answer asap to get a upvote
Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(X₁₁X2 X3 X4) = (x₁ + x2,0,X3 + X4 X3 +X4) a. Is the linear transformation one-to-one? OA. T is one-to-one because the column vectors are not scalar multiples of each other. OB. T is one-to-one because T(x) = 0 has only the trivial solution. OC. T is not one-to-one because the standard matrix A has a free variable. OD. T is not one-to-one because the columns of the standard matrix A are linearly independent. b. Is the linear transformation onto? OA. T is onto because the columns of the standard matrix A span R4. " B. T is not onto because the second row of the standard matrix A is all zeros. 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 columns of the standard matrix A span R4. ... CS Scanned with CamScanner
Transcribed Image Text:Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(X₁₁X2 X3 X4) = (x₁ + x2,0,X3 + X4 X3 +X4) a. Is the linear transformation one-to-one? OA. T is one-to-one because the column vectors are not scalar multiples of each other. OB. T is one-to-one because T(x) = 0 has only the trivial solution. OC. T is not one-to-one because the standard matrix A has a free variable. OD. T is not one-to-one because the columns of the standard matrix A are linearly independent. b. Is the linear transformation onto? OA. T is onto because the columns of the standard matrix A span R4. " B. T is not onto because the second row of the standard matrix A is all zeros. 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 columns of the standard matrix A span R4. ... CS Scanned with CamScanner
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