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Let V be the vector space of all 2 x 2 matrix over the field R of real numbers and B = 
. If T : V--> V is a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?
. If T : V--> V is a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let V be the vector space of all 2 x 2 matrix over the field R of real...
Let V be the vector space of all 2 x 2 matrices over the field R of real numbers and matrix
Let T : V —> V be a linear transformation defined by T(A) = AB - BA
We need to determine the dim of ker T.
Let
Then, take T(A) = 0 implies AB - BA = 0
Substituting the values of matrices A and B,
we get
or equivalently
=
or equivalently
implies c =0 and a + b - d = 0 Therefore,
Hence, dim (ker T) = Total number of variables - Number of restrictions = 4 - 2 = 2
Let T : V —> V be a linear transformation defined by T(A) = AB - BA
We need to determine the dim of ker T.
Let
Then, take T(A) = 0 implies AB - BA = 0
Substituting the values of matrices A and B,
we get
or equivalently
=
or equivalently
implies c =0 and a + b - d = 0 Therefore,
Hence, dim (ker T) = Total number of variables - Number of restrictions = 4 - 2 = 2
Most Upvoted Answer
Let V be the vector space of all 2 x 2 matrix over the field R of real...
Let V be the vector space of all 2 x 2 matrices over the field R of real numbers and matrix
Let T : V —> V be a linear transformation defined by T(A) = AB - BA
We need to determine the dim of ker T.
Let
Then, take T(A) = 0 implies AB - BA = 0
Substituting the values of matrices A and B,
we get
or equivalently
=
or equivalently
implies c =0 and a + b - d = 0 Therefore,
Hence, dim (ker T) = Total number of variables - Number of restrictions = 4 - 2 = 2
Let T : V —> V be a linear transformation defined by T(A) = AB - BA
We need to determine the dim of ker T.
Let
Then, take T(A) = 0 implies AB - BA = 0
Substituting the values of matrices A and B,
we get
or equivalently
=
or equivalently
implies c =0 and a + b - d = 0 Therefore,
Hence, dim (ker T) = Total number of variables - Number of restrictions = 4 - 2 = 2
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Let V be the vector space of all 2 x 2 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?
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Let V be the vector space of all 2 x 2 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. 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 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. 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 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?.
Let V be the vector space of all 2 x 2 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. 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 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. 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 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?.
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Let V be the vector space of all 2 x 2 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Let V be the vector space of all 2 x 2 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Let V be the vector space of all 2 x 2 matrix over the field R of real numbers and B = . If T: V--> Vis a linear transformation defined by T(A) = AB - BA, then what is the dimension of the Kernel of T?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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