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Consider the mapping
Q. Which of the above are linear transformation?
Q. Which of the above are linear transformation?
- a)I, II and III
- b)I and II, only
- c)II and III only
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the mappingQ. Which of the above are linear transforma...
I. We are given that the transformation T: R3 —> R2 defined by
T (x , y , z) = (x + 1, y + z)
We need to determine the linearity of the given linear transformation.
Now,T'(0, 0, 0) = (1, 0)
Since the image of (0, 0,0) under transformation T is (1, 0) which is not the zero of R2.
Hence, T is non-linear.
II. We are given that the transformation T : R3 --> R defined by
T(x,y,z) = (xy)
We need to determine the linearity of this given transformation.
Since the image of (x, y, z) under linear transformation.
T is an algebraic term of degree 2.
Therefore, T is non linear.
III. We are given that the transformation T: R3 —> R2 defined by
T(x, y, z) = (| x |, 0)
We need to determine the linearity of this linear transformation
Let (1, 0, 0) and (-1, 0, 0) be two vectors of R3
Then T(l,0,0) = (l,0)
andT(-l, 0, 0) = (1, 0)
Now,T [(1, 0, 0) + (-1, 0, 0)] =
T(0, 0, 0) = (0, 0)
and T(1, 0, 0) + T(-1, 0, 0)
= (1, 0) + (1,0) = (2, 0)
Hence, T [(1, 0, 0) + (-1, 0, 0)] ≠ T{ 1, 0, 0) + T (-1, 0, 0).
Therefore, T is non linear.
T (x , y , z) = (x + 1, y + z)
We need to determine the linearity of the given linear transformation.
Now,T'(0, 0, 0) = (1, 0)
Since the image of (0, 0,0) under transformation T is (1, 0) which is not the zero of R2.
Hence, T is non-linear.
II. We are given that the transformation T : R3 --> R defined by
T(x,y,z) = (xy)
We need to determine the linearity of this given transformation.
Since the image of (x, y, z) under linear transformation.
T is an algebraic term of degree 2.
Therefore, T is non linear.
III. We are given that the transformation T: R3 —> R2 defined by
T(x, y, z) = (| x |, 0)
We need to determine the linearity of this linear transformation
Let (1, 0, 0) and (-1, 0, 0) be two vectors of R3
Then T(l,0,0) = (l,0)
andT(-l, 0, 0) = (1, 0)
Now,T [(1, 0, 0) + (-1, 0, 0)] =
T(0, 0, 0) = (0, 0)
and T(1, 0, 0) + T(-1, 0, 0)
= (1, 0) + (1,0) = (2, 0)
Hence, T [(1, 0, 0) + (-1, 0, 0)] ≠ T{ 1, 0, 0) + T (-1, 0, 0).
Therefore, T is non linear.
Most Upvoted Answer
Consider the mappingQ. Which of the above are linear transforma...
I. We are given that the transformation T: R3 —> R2 defined by
T (x , y , z) = (x + 1, y + z)
We need to determine the linearity of the given linear transformation.
Now,T'(0, 0, 0) = (1, 0)
Since the image of (0, 0,0) under transformation T is (1, 0) which is not the zero of R2.
Hence, T is non-linear.
II. We are given that the transformation T : R3 --> R defined by
T(x,y,z) = (xy)
We need to determine the linearity of this given transformation.
Since the image of (x, y, z) under linear transformation.
T is an algebraic term of degree 2.
Therefore, T is non linear.
III. We are given that the transformation T: R3 —> R2 defined by
T(x, y, z) = (| x |, 0)
We need to determine the linearity of this linear transformation
Let (1, 0, 0) and (-1, 0, 0) be two vectors of R3
Then T(l,0,0) = (l,0)
andT(-l, 0, 0) = (1, 0)
Now,T [(1, 0, 0) + (-1, 0, 0)] =
T(0, 0, 0) = (0, 0)
and T(1, 0, 0) + T(-1, 0, 0)
= (1, 0) + (1,0) = (2, 0)
Hence, T [(1, 0, 0) + (-1, 0, 0)] ≠ T{ 1, 0, 0) + T (-1, 0, 0).
Therefore, T is non linear.
T (x , y , z) = (x + 1, y + z)
We need to determine the linearity of the given linear transformation.
Now,T'(0, 0, 0) = (1, 0)
Since the image of (0, 0,0) under transformation T is (1, 0) which is not the zero of R2.
Hence, T is non-linear.
II. We are given that the transformation T : R3 --> R defined by
T(x,y,z) = (xy)
We need to determine the linearity of this given transformation.
Since the image of (x, y, z) under linear transformation.
T is an algebraic term of degree 2.
Therefore, T is non linear.
III. We are given that the transformation T: R3 —> R2 defined by
T(x, y, z) = (| x |, 0)
We need to determine the linearity of this linear transformation
Let (1, 0, 0) and (-1, 0, 0) be two vectors of R3
Then T(l,0,0) = (l,0)
andT(-l, 0, 0) = (1, 0)
Now,T [(1, 0, 0) + (-1, 0, 0)] =
T(0, 0, 0) = (0, 0)
and T(1, 0, 0) + T(-1, 0, 0)
= (1, 0) + (1,0) = (2, 0)
Hence, T [(1, 0, 0) + (-1, 0, 0)] ≠ T{ 1, 0, 0) + T (-1, 0, 0).
Therefore, T is non linear.
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Consider the mappingQ. Which of the above are linear transformation?a)I, II and IIIb)I and II, onlyc)II and III onlyd)None of theseCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Consider the mappingQ. Which of the above are linear transformation?a)I, II and IIIb)I and II, onlyc)II and III onlyd)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the mappingQ. Which of the above are linear transformation?a)I, II and IIIb)I and II, onlyc)II and III onlyd)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Consider the mappingQ. Which of the above are linear transformation?a)I, II and IIIb)I and II, onlyc)II and III onlyd)None of theseCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Consider the mappingQ. Which of the above are linear transformation?a)I, II and IIIb)I and II, onlyc)II and III onlyd)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the mappingQ. Which of the above are linear transformation?a)I, II and IIIb)I and II, onlyc)II and III onlyd)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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