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Let T : R2-->R 2 be a map defined by
T(x,y) = (x + y , x - y)
Which of the following statement is correct?
  • a)
    T is linear and its kernel has infinite number of elements of R2
  • b)
    T is non linear
  • c)
    The kernel of T consist of only two elements of R2
  • d)
    Nullity of T is zero
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let T : R2-->R 2 be a map defined byT(x,y) = (x + y , x - y)Which o...
We are given that a linear transformation T : R2—> R2 is defined by
T(x,y) = (x + y , x - y)

= αT(x1
,
y
1) + βT(x2, y2)
Hence, T is a linear transformation.
Let (x, y) ∈ ker T Then T(x, y) = (0, 0) Implies(x + y , x —y) = (0, 0)
Implies x +y = 0 and x - y = 0
Solving for x and y, we get
x = 0, y = 0
Hence ker T= {0, 0}
Therefore,
Nullity of T= dim ker T = 0
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Most Upvoted Answer
Let T : R2-->R 2 be a map defined byT(x,y) = (x + y , x - y)Which o...
We are given that a linear transformation T : R2—> R2 is defined by
T(x,y) = (x + y , x - y)

= αT(x1
,
y
1) + βT(x2, y2)
Hence, T is a linear transformation.
Let (x, y) ∈ ker T Then T(x, y) = (0, 0) Implies(x + y , x —y) = (0, 0)
Implies x +y = 0 and x - y = 0
Solving for x and y, we get
x = 0, y = 0
Hence ker T= {0, 0}
Therefore,
Nullity of T= dim ker T = 0
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Community Answer
Let T : R2-->R 2 be a map defined byT(x,y) = (x + y , x - y)Which o...
R2 be a linear transformation. The transformation T can be represented by a 2x2 matrix.
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Let T : R2-->R 2 be a map defined byT(x,y) = (x + y , x - y)Which of the following statement is correct?a)T is linear and its kernel has infinite number of elements of R2b)T is non linearc)The kernel of T consist of only two elements of R2d)Nullity of T is zeroCorrect answer is option 'D'. Can you explain this answer?
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Let T : R2-->R 2 be a map defined byT(x,y) = (x + y , x - y)Which of the following statement is correct?a)T is linear and its kernel has infinite number of elements of R2b)T is non linearc)The kernel of T consist of only two elements of R2d)Nullity of T is zeroCorrect answer is option 'D'. 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 Let T : R2-->R 2 be a map defined byT(x,y) = (x + y , x - y)Which of the following statement is correct?a)T is linear and its kernel has infinite number of elements of R2b)T is non linearc)The kernel of T consist of only two elements of R2d)Nullity of T is zeroCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let T : R2-->R 2 be a map defined byT(x,y) = (x + y , x - y)Which of the following statement is correct?a)T is linear and its kernel has infinite number of elements of R2b)T is non linearc)The kernel of T consist of only two elements of R2d)Nullity of T is zeroCorrect answer is option 'D'. Can you explain this answer?.
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