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Let V be a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If 
, then
, then- a)V = A -B
- b)V = A +B
- c)dim(A + B) ≤ 3
- d)dim( A ∩ B) ≠ 0
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let V be a 3 dimensional vector space with A and B its subspaces of di...
We know
dim A + dim B = dim (A + B) + dim (A ∩ B ) .............. (1)
Here A ∩) B = { 0 } => dim (A ∩ B ) = 0
then by equation (1), dim (A + B ) = 3 => option (C) and (D) are incorrect.
Now (A + B) be a subspace of V and has same dimension as V.
=> V = A + B
Most Upvoted Answer
Let V be a 3 dimensional vector space with A and B its subspaces of di...
We know
dim A + dim B = dim (A + B) + dim (A ∩ B ) .............. (1)
Here A ∩) B = { 0 } => dim (A ∩ B ) = 0
then by equation (1), dim (A + B ) = 3 => option (C) and (D) are incorrect.
Now (A + B) be a subspace of V and has same dimension as V.
=> V = A + B
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Let V be a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If, thena)V = A -Bb)V = A +Bc)dim(A + B) ≤ 3d)dim( A ∩ B) ≠ 0Correct answer is option 'B'. Can you explain this answer?
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Let V be a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If, thena)V = A -Bb)V = A +Bc)dim(A + B) ≤ 3d)dim( A ∩ B) ≠ 0Correct 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 a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If, thena)V = A -Bb)V = A +Bc)dim(A + B) ≤ 3d)dim( A ∩ B) ≠ 0Correct 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 a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If, thena)V = A -Bb)V = A +Bc)dim(A + B) ≤ 3d)dim( A ∩ B) ≠ 0Correct answer is option 'B'. Can you explain this answer?.
Let V be a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If, thena)V = A -Bb)V = A +Bc)dim(A + B) ≤ 3d)dim( A ∩ B) ≠ 0Correct 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 a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If, thena)V = A -Bb)V = A +Bc)dim(A + B) ≤ 3d)dim( A ∩ B) ≠ 0Correct 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 a 3 dimensional vector space with A and B its subspaces of dimensions 2 and 1 , respectively. If, thena)V = A -Bb)V = A +Bc)dim(A + B) ≤ 3d)dim( A ∩ B) ≠ 0Correct answer is option 'B'. Can you explain this answer?.
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