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Let Mn(R) denote the space of all nxn matrices with entries in a field 
. Fix a non-singular matrix 
and consider the map 
given by, 
then
. Fix a non-singular matrix and consider the map given by, then- a)
- b)
- c)Rank of T is n2
- d)T is non-singular
Correct answer is option 'A,C,D'. Can you explain this answer?
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Verified Answer
Let Mn(R) denote the space of all nxn matrices with entries in a field...
We can solve it by taking example,
be a non singular matrixThen T : M2(k) by
T(x) = Ax
now
Thus matrix representation of T relative to the standard basis
⇒ Trace (T) = 6 = 2(2 + 1)
⇒ option (A) is correct.
Rank o f T is 4 i.e. 22 .
Rank o f T is 4 i.e. 22 .
=> Rank of T is n2 .
Clearly T is non - singular.
Clearly T is non - singular.
Most Upvoted Answer
Let Mn(R) denote the space of all nxn matrices with entries in a field...
We can solve it by taking example,
be a non singular matrixThen T : M2(k) by
T(x) = Ax
now
Thus matrix representation of T relative to the standard basis
⇒ Trace (T) = 6 = 2(2 + 1)
⇒ option (A) is correct.
Rank o f T is 4 i.e. 22 .
Rank o f T is 4 i.e. 22 .
=> Rank of T is n2 .
Clearly T is non - singular.
Clearly T is non - singular.
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Let Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. Can you explain this answer?
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Let Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. 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 Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. 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 Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. Can you explain this answer?.
Let Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. 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 Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. 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 Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. Can you explain this answer?.
Solutions for Let Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Let Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. Can you explain this answer?, a detailed solution for Let Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. Can you explain this answer? has been provided alongside types of Let Mn(R) denote the space of all nxn matrices with entries in a field . Fix a non-singular matrixand consider the mapgiven by,thena)b)c)Rank of T is n2d)T is non-singularCorrect answer is option 'A,C,D'. Can you explain this answer? theory, EduRev gives you an
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