Mathematics Exam > Mathematics Questions > Let T: R3 → R3 be a linear transformatio...
Start Learning for Free
Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)
- a)cannot be 0
- b)cannot be 2
- c)cannot be 3
- d)cannot be 1
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let T: R3 → R3 be a linear transformation and I be the identify t...
By rank-nullity is theorem,
dim(T) = Rank(T) + Nullity (T)
Here dim(T) = 3 Now, (T – CI)x = T(x) – (T(x) = cx – cx
= 0
(I is identity transformation)
⇒ Nullity of T – CI cannot be zero
⇒ Hence, Rank of T – CI cannot be 3.
dim(T) = Rank(T) + Nullity (T)
Here dim(T) = 3 Now, (T – CI)x = T(x) – (T(x) = cx – cx
= 0
(I is identity transformation)
⇒ Nullity of T – CI cannot be zero
⇒ Hence, Rank of T – CI cannot be 3.
Most Upvoted Answer
Let T: R3 → R3 be a linear transformation and I be the identify t...
By rank-nullity is theorem,
dim(T) = Rank(T) + Nullity (T)
Here dim(T) = 3 Now, (T – CI)x = T(x) – (T(x) = cx – cx
= 0
(I is identity transformation)
⇒ Nullity of T – CI cannot be zero
⇒ Hence, Rank of T – CI cannot be 3.
dim(T) = Rank(T) + Nullity (T)
Here dim(T) = 3 Now, (T – CI)x = T(x) – (T(x) = cx – cx
= 0
(I is identity transformation)
⇒ Nullity of T – CI cannot be zero
⇒ Hence, Rank of T – CI cannot be 3.
Free Test
FREE
| Start Free Test |
Community Answer
Let T: R3 → R3 be a linear transformation and I be the identify t...
Let T: R3 -> R3 be a linear transformation.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. Can you explain this answer?
Question Description
Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. 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: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. 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: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. Can you explain this answer?.
Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. 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: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. 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: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. Can you explain this answer?.
Solutions for Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. 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 Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let T: R3 → R3 be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a non-zero vector x ∈ R3 such that T(x) = Cx, then rank (T – CI)a)cannot be 0b)cannot be 2c)cannot be 3d)cannot be 1Correct answer is option 'C'. 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