Mathematics Exam > Mathematics Questions > Let V be the vector space of all 2 x 2 matric...
Start Learning for Free
Let V be the vector space of all 2 x 2 matrices over the field R of real numbers and 
is a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?
is a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let V be the vector space of all 2 x 2 matrices over the field R of re...
Let U (F) and V(F) be two vector spaces and let T be a linear transformation from U to V, then the null space of T written as N(T) is the set of all vectors a in U such that T(α) = Of zero vector of V)
The null space of T is also called the kernel of T.
Now the standard basis for a vector space of all 2x2 matrices over field R of real number is {e1, e2, e3, e4}
where
we have, T(A) = AB - BA, where B =
so,
Thus. T (e1), T(e2), T(e3) and T(e4) span the range of T
Null space
let
∈ null space of T
This system of equations have two independent variables hence, it have two independent solutions.
⇒ The dimension of null space is 2.
The null space of T is also called the kernel of T.
Now the standard basis for a vector space of all 2x2 matrices over field R of real number is {e1, e2, e3, e4}
where
we have, T(A) = AB - BA, where B =
so,
Thus. T (e1), T(e2), T(e3) and T(e4) span the range of T
Null space
let
∈ null space of TThis system of equations have two independent variables hence, it have two independent solutions.
⇒ The dimension of null space is 2.
Most Upvoted Answer
Let V be the vector space of all 2 x 2 matrices over the field R of re...
Let U (F) and V(F) be two vector spaces and let T be a linear transformation from U to V, then the null space of T written as N(T) is the set of all vectors a in U such that T(α) = Of zero vector of V)
The null space of T is also called the kernel of T.
Now the standard basis for a vector space of all 2x2 matrices over field R of real number is {e1, e2, e3, e4}
where
we have, T(A) = AB - BA, where B =
so,
Thus. T (e1), T(e2), T(e3) and T(e4) span the range of T
Null space
let
∈ null space of T
This system of equations have two independent variables hence, it have two independent solutions.
⇒ The dimension of null space is 2.
The null space of T is also called the kernel of T.
Now the standard basis for a vector space of all 2x2 matrices over field R of real number is {e1, e2, e3, e4}
where
we have, T(A) = AB - BA, where B =
so,
Thus. T (e1), T(e2), T(e3) and T(e4) span the range of T
Null space
let
∈ null space of TThis system of equations have two independent variables hence, it have two independent solutions.
⇒ The dimension of null space is 2.
Free Test
FREE
| Start Free Test |
Community Answer
Let V be the vector space of all 2 x 2 matrices over the field R of re...
Let U (F) and V(F) be two vector spaces and let T be a linear transformation from U to V, then the null space of T written as N(T) is the set of all vectors a in U such that T(α) = Of zero vector of V)
The null space of T is also called the kernel of T.
Now the standard basis for a vector space of all 2x2 matrices over field R of real number is {e1, e2, e3, e4}
where
we have, T(A) = AB - BA, where B =
so,
Thus. T (e1), T(e2), T(e3) and T(e4) span the range of T
Null space
let ∈ null space of T
This system of equations have two independent variables hence, it have two independent solutions.
⇒ The dimension of null space is 2.
The null space of T is also called the kernel of T.
Now the standard basis for a vector space of all 2x2 matrices over field R of real number is {e1, e2, e3, e4}
where
we have, T(A) = AB - BA, where B =
so,
Thus. T (e1), T(e2), T(e3) and T(e4) span the range of T
Null space
let
∈ null space of TThis system of equations have two independent variables hence, it have two independent solutions.
⇒ The dimension of null space is 2.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Let V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. Can you explain this answer?
Question Description
Let V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. 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 V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. 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 V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. Can you explain this answer?.
Let V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. 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 V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. 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 V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. Can you explain this answer?.
Solutions for Let V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. 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 V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. Can you explain this answer?, a detailed solution for Let V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. Can you explain this answer? has been provided alongside types of Let V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let V be the vector space of all 2 x 2 matrices over the field R of real numbers andis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the kernel of T?Correct answer is '2'. 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