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The transformation T : R3 → R2 defined by, 
T(x,y,z) = (x +y, y+z) is,
  • a)
    Linear and has zero kernel.
  • b)
    Linear and has a proper subspace as kernel.
  • c)
    Linear and one to one.
  • d)
    Linear and kernel be a improper subspace of R3.
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The transformation T : R3→R2 defined by,T(x,y,z) = (x +y, y+z) is...



⇒ T is linear 
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The transformation T : R3→R2 defined by,T(x,y,z) = (x +y, y+z) is...
To R2 is defined by T(x, y, z) = (x + y, x - z). This means that for any vector (x, y, z) in R3, the transformation T maps it to the vector (x + y, x - z) in R2.
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The transformation T : R3→R2 defined by,T(x,y,z) = (x +y, y+z) is,a)Linear and has zero kernel.b)Linear and has a proper subspace as kernel.c)Linear and one to one.d)Linear and kernel be a improper subspace of R3.Correct answer is option 'B'. Can you explain this answer?
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The transformation T : R3→R2 defined by,T(x,y,z) = (x +y, y+z) is,a)Linear and has zero kernel.b)Linear and has a proper subspace as kernel.c)Linear and one to one.d)Linear and kernel be a improper subspace of R3.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 The transformation T : R3→R2 defined by,T(x,y,z) = (x +y, y+z) is,a)Linear and has zero kernel.b)Linear and has a proper subspace as kernel.c)Linear and one to one.d)Linear and kernel be a improper subspace of R3.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 The transformation T : R3→R2 defined by,T(x,y,z) = (x +y, y+z) is,a)Linear and has zero kernel.b)Linear and has a proper subspace as kernel.c)Linear and one to one.d)Linear and kernel be a improper subspace of R3.Correct answer is option 'B'. Can you explain this answer?.
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