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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?
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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.
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Let T: R3 → R3 be a linear transformation and I be the identify t...
Let T: R3 -> R3 be a linear transformation.
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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?
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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?.
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