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If the linear transformation T(v) = Av rotates the vectors v1 = (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:
- a)T(v1) = (1, 0) and T(v2) = (0, -1)
- b)T(v1) = (-1,0 )and T(v2) = (0, 1)
- c)T(v,) = (0, 1)and T(v2) = (1,0)
- d)T(v1) = (0, -1) and T(v2) = (-1,0)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0)...
We are give that the linear transformation T(v) = Av rotates the vectors v1 = (-1,0) and v2 = (0,1) clockwise π radians. We need to find the image of v1 = (-1, 0) and v2 = (0,1) under T
We know that if a vector (a, b) is rotated through an angle α under linear transformation T, then
Here v1 = (-1, 0) and a = π
Therefore,v2 = (0,1)
= (1,0)
and T(v2) = T(0, 1)
= (0,-1)
We know that if a vector (a, b) is rotated through an angle α under linear transformation T, then
Here v1 = (-1, 0) and a = πTherefore,v2 = (0,1)
= (1,0)
and T(v2) = T(0, 1)
= (0,-1)
Most Upvoted Answer
If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0)...
If the linear transformation T(v) = Av rotates the vectors v1 = (-1, 0) and v2 = (0, 1) clockwise, then the matrix A representing the transformation can be found by considering the images of these vectors.
First, let's find the image of v1 = (-1, 0) under the transformation T.
T(v1) = A * v1
Since v1 = (-1, 0), we have:
T(v1) = A * (-1, 0)
Next, let's find the image of v2 = (0, 1) under the transformation T.
T(v2) = A * v2
Since v2 = (0, 1), we have:
T(v2) = A * (0, 1)
By considering the clockwise rotation, we can deduce that the image of v1 should be (0, 1) and the image of v2 should be (1, 0).
Therefore, we can set up the following equations:
A * (-1, 0) = (0, 1)
A * (0, 1) = (1, 0)
Multiplying these equations out, we get:
(-A, 0) = (0, 1)
(0, A) = (1, 0)
From the first equation, we can see that A must be 0. From the second equation, we see that A must be 1.
Since these equations contradict each other, it is not possible to find a matrix A that rotates the vectors v1 and v2 clockwise.
First, let's find the image of v1 = (-1, 0) under the transformation T.
T(v1) = A * v1
Since v1 = (-1, 0), we have:
T(v1) = A * (-1, 0)
Next, let's find the image of v2 = (0, 1) under the transformation T.
T(v2) = A * v2
Since v2 = (0, 1), we have:
T(v2) = A * (0, 1)
By considering the clockwise rotation, we can deduce that the image of v1 should be (0, 1) and the image of v2 should be (1, 0).
Therefore, we can set up the following equations:
A * (-1, 0) = (0, 1)
A * (0, 1) = (1, 0)
Multiplying these equations out, we get:
(-A, 0) = (0, 1)
(0, A) = (1, 0)
From the first equation, we can see that A must be 0. From the second equation, we see that A must be 1.
Since these equations contradict each other, it is not possible to find a matrix A that rotates the vectors v1 and v2 clockwise.
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If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)Correct answer is option 'A'. Can you explain this answer?
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If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)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 If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)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 If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)Correct answer is option 'A'. Can you explain this answer?.
If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)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 If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)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 If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)Correct answer is option 'A'. Can you explain this answer?.
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If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the linear transformation T(v) = Av rotates the vectors v1= (-1, 0) and v2 = (0, 1) clockwise π radians, the resulting vectors are:a)T(v1) = (1, 0) and T(v2) = (0, -1)b)T(v1) = (-1,0 )and T(v2) = (0, 1)c)T(v,) = (0, 1)and T(v2) = (1,0)d)T(v1) = (0, -1) and T(v2) = (-1,0)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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