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If the linear transformation T : R2 → R3 is such that T(1, 0) = (2,3,1) and T(1,1) = (3, 0,2), then
  • a)
    T(x, y) = (x +y, 2x + y, 3x - 3y)
  • b)
    T(x, y) = (2x + y, 3x - 3y, x +y)
  • c)
    T(x, y) = (2x - y, 3x + 3y, x - y)
  • d)
    T(x, y) = (x - y, 2x - y , 3x + 3y)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the linear transformation T : R2 → R3 is such that T(1, 0) = (...
We are given that a linear transformation T : R3→ R3 defined by
T(1, 0) = (2, 3,1)
and T(l, 1) = (3, 0, 2)
We need to find the image of (x, y) under linear transformation T.
Let there exist scalars α and β such that
(x,y) = α(1,0) + β(1, 1) 
or equivalently (x, y)= (α + β, β)
Comparing the components on both sides, we get
x = α + β and y = β
Solving for α and β, we get
α = x - y and β = y
Therefore,(x, y)= (x - y) (1, 0) + y(1, 1) Taking the image under linear transformation T. we get

implies T(x, y) = (2x + y, 3x - 3y, x+y).
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Most Upvoted Answer
If the linear transformation T : R2 → R3 is such that T(1, 0) = (...
We are given that a linear transformation T : R3→ R3 defined by
T(1, 0) = (2, 3,1)
and T(l, 1) = (3, 0, 2)
We need to find the image of (x, y) under linear transformation T.
Let there exist scalars α and β such that
(x,y) = α(1,0) + β(1, 1) 
or equivalently (x, y)= (α + β, β)
Comparing the components on both sides, we get
x = α + β and y = β
Solving for α and β, we get
α = x - y and β = y
Therefore,(x, y)= (x - y) (1, 0) + y(1, 1) Taking the image under linear transformation T. we get

implies T(x, y) = (2x + y, 3x - 3y, x+y).
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If the linear transformation T : R2 → R3 is such that T(1, 0) = (2,3,1) and T(1,1) = (3, 0,2), thena)T(x, y) = (x +y, 2x + y, 3x - 3y)b)T(x, y) = (2x + y, 3x - 3y, x +y)c)T(x, y) = (2x - y, 3x + 3y, x - y)d)T(x, y) = (x - y, 2x - y , 3x + 3y)Correct answer is option 'B'. Can you explain this answer?
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If the linear transformation T : R2 → R3 is such that T(1, 0) = (2,3,1) and T(1,1) = (3, 0,2), thena)T(x, y) = (x +y, 2x + y, 3x - 3y)b)T(x, y) = (2x + y, 3x - 3y, x +y)c)T(x, y) = (2x - y, 3x + 3y, x - y)d)T(x, y) = (x - y, 2x - y , 3x + 3y)Correct answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If the linear transformation T : R2 → R3 is such that T(1, 0) = (2,3,1) and T(1,1) = (3, 0,2), thena)T(x, y) = (x +y, 2x + y, 3x - 3y)b)T(x, y) = (2x + y, 3x - 3y, x +y)c)T(x, y) = (2x - y, 3x + 3y, x - y)d)T(x, y) = (x - y, 2x - y , 3x + 3y)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the linear transformation T : R2 → R3 is such that T(1, 0) = (2,3,1) and T(1,1) = (3, 0,2), thena)T(x, y) = (x +y, 2x + y, 3x - 3y)b)T(x, y) = (2x + y, 3x - 3y, x +y)c)T(x, y) = (2x - y, 3x + 3y, x - y)d)T(x, y) = (x - y, 2x - y , 3x + 3y)Correct answer is option 'B'. Can you explain this answer?.
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