Mathematics Exam > Mathematics Questions > If the linear transformation T(v) = Av rotate...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
|
Explore Courses for Mathematics exam
|
|
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning 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? defined & explained in the simplest way possible. Besides giving the explanation 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?, 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
ample number of questions to practice 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? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup