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
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 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.
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