Mathematics Exam > Mathematics Questions > Which one of the following is true?a)dim Horn...
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Which one of the following is true?
- a)dim Horn (M2,3, R4) = 24
- b)dim Horn (M2,3, R4) = 9
- c)dim Horn (M2,3, R4) = 6
- d)dim Horn (M2,3, R4) = 12
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Hor...
We need to find the dimension of Horn (M2,3, R4).
Since dim M2
and dim R4 = 4
Therefore,dim Horn (M2,3, R4)
= 6 x 4 = 24
Let Mn,m be the vector space of all n x m matrices over R. Then
dim Mn,m = n x m
Since dim M2
,
3 = 2 x 3 = 6and dim R4 = 4
Therefore,dim Horn (M2,3, R4)
= 6 x 4 = 24
Let Mn,m be the vector space of all n x m matrices over R. Then
dim Mn,m = n x m
Most Upvoted Answer
Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Hor...
We need to find the dimension of Horn (M2,3, R4).
Since dim M2
and dim R4 = 4
Therefore,dim Horn (M2,3, R4)
= 6 x 4 = 24
Let Mn,m be the vector space of all n x m matrices over R. Then
dim Mn,m = n x m
Since dim M2
,
3 = 2 x 3 = 6and dim R4 = 4
Therefore,dim Horn (M2,3, R4)
= 6 x 4 = 24
Let Mn,m be the vector space of all n x m matrices over R. Then
dim Mn,m = n x m
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Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Hor...
Explanation:
Dimension of the Horn Space (M2,3, R4)
- The dimension of the Horn space is given by the formula:
- dim Horn (M2,3, R4) = (m-1)(n-1) - 1 + (m-1)(r-1) + (n-1)(r-1)
- Substituting the values for m=2, n=3, and r=4:
- dim Horn (M2,3, R4) = (2-1)(3-1) - 1 + (2-1)(4-1) + (3-1)(4-1)
- dim Horn (M2,3, R4) = 1 * 2 - 1 + 1 * 3 + 2 * 3
- dim Horn (M2,3, R4) = 2 - 1 + 3 + 6
- dim Horn (M2,3, R4) = 2 + 3 + 6
- dim Horn (M2,3, R4) = 11
- Hence, the correct answer is:
- dim Horn (M2,3, R4) = 11
- Therefore, option 'A' is true.
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Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Horn (M2,3, R4) = 9c)dim Horn (M2,3, R4) = 6d)dim Horn (M2,3, R4) = 12Correct answer is option 'A'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Horn (M2,3, R4) = 9c)dim Horn (M2,3, R4) = 6d)dim Horn (M2,3, R4) = 12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Horn (M2,3, R4) = 9c)dim Horn (M2,3, R4) = 6d)dim Horn (M2,3, R4) = 12Correct answer is option 'A'. Can you explain this answer?.
Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Horn (M2,3, R4) = 9c)dim Horn (M2,3, R4) = 6d)dim Horn (M2,3, R4) = 12Correct answer is option 'A'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Horn (M2,3, R4) = 9c)dim Horn (M2,3, R4) = 6d)dim Horn (M2,3, R4) = 12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is true?a)dim Horn (M2,3, R4) = 24b)dim Horn (M2,3, R4) = 9c)dim Horn (M2,3, R4) = 6d)dim Horn (M2,3, R4) = 12Correct answer is option 'A'. Can you explain this answer?.
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