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Let Vbe a vector space over (ℝ) of dimension 7 and T :V → ℝ be a non-zero linear transformation. Let W be a linear subsapce of V such that V = ker (T) ⊕ W, Where ker (T) denotes the null space of T. Then dimension of W is (Answer should be integer)___________.
Correct answer is '1'. Can you explain this answer?
Most Upvoted Answer
Let Vbe a vector space over () of dimension 7 and T :V →be a non-...
Let T:V → ℝ be a non zero linear transformation, then rank (T) = 1. Hence Ker(T) = 7 - 1=6
Given V = Ker(T)⊕W
⇒ dim(V) = dim(ker(T)) + dim(W)
⇒ 7 = 6+ dim(W)
⇒ dim(W) =1
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Let Vbe a vector space over () of dimension 7 and T :V →be a non-zero linear transformation. Let W be a linear subsapce of V such that V = ker (T)⊕ W, Where ker (T) denotes the null space of T. Then dimension of W is (Answer should be integer)___________.Correct answer is '1'. Can you explain this answer?
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