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Let T : R2 → R2 be a linear transformation such that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4).Then T((5, -4)) is
- a)(-4, -41)
- b)(-6, 1)
- c)(-1, 6)
- d)(1, -6)
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Let T : R2 → R2 be a linear transformation such that T((1, 2)) = ...
Given, T((1, 2)) = (2, 3) and
T((0, 1)) = (1, 4)
As T is the linear transformation
⇒ T(av1 + bv2) = a T(v1) + b T(v2).
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Community Answer
Let T : R2 → R2 be a linear transformation such that T((1, 2)) = ...
Given Information:
- T((1, 2)) = (2, 3)
- T((0, 1)) = (1, 4)
Calculating T((5, -4)):
- Since T is a linear transformation, we can express any vector in R2 as a linear combination of the basis vectors (1, 0) and (0, 1).
- Therefore, we can express (5, -4) as 5*(1, 0) + (-4)*(0, 1) = (5, 0) + (0, -4) = (5, -4).
- Using the linearity property of T, we have:
T((5, -4)) = T(5*(1, 0) + (-4)*(0, 1))
= 5*T((1, 0)) + (-4)*T((0, 1))
= 5*(2, 3) + (-4)*(1, 4)
= (10, 15) + (-4, -16)
= (10 - 4, 15 - 16)
= (6, -1)
Conclusion:
- Therefore, T((5, -4)) = (6, -1), which does not match any of the given answer options.
- However, this might be a case of a typographical error in the given options, as the correct calculation yields a different result.
- T((1, 2)) = (2, 3)
- T((0, 1)) = (1, 4)
Calculating T((5, -4)):
- Since T is a linear transformation, we can express any vector in R2 as a linear combination of the basis vectors (1, 0) and (0, 1).
- Therefore, we can express (5, -4) as 5*(1, 0) + (-4)*(0, 1) = (5, 0) + (0, -4) = (5, -4).
- Using the linearity property of T, we have:
T((5, -4)) = T(5*(1, 0) + (-4)*(0, 1))
= 5*T((1, 0)) + (-4)*T((0, 1))
= 5*(2, 3) + (-4)*(1, 4)
= (10, 15) + (-4, -16)
= (10 - 4, 15 - 16)
= (6, -1)
Conclusion:
- Therefore, T((5, -4)) = (6, -1), which does not match any of the given answer options.
- However, this might be a case of a typographical error in the given options, as the correct calculation yields a different result.
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Let T : R2 → R2 be a linear transformation such that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4).Then T((5, -4)) isa)(-4, -41)b)(-6, 1)c)(-1, 6)d)(1, -6)Correct answer is option 'A'. Can you explain this answer?
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Let T : R2 → R2 be a linear transformation such that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4).Then T((5, -4)) isa)(-4, -41)b)(-6, 1)c)(-1, 6)d)(1, -6)Correct answer is option 'A'. 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 → R2 be a linear transformation such that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4).Then T((5, -4)) isa)(-4, -41)b)(-6, 1)c)(-1, 6)d)(1, -6)Correct answer is option 'A'. 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 → R2 be a linear transformation such that T((1, 2)) = (2, 3) and T((0, 1)) = (1, 4).Then T((5, -4)) isa)(-4, -41)b)(-6, 1)c)(-1, 6)d)(1, -6)Correct answer is option 'A'. Can you explain this answer?.
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