be a vector space of all 2x2 real square matrices over field . Let Wbe a subspace oflet W is span by the setbe afixed matrix.Letbe a L.T. defined bythen the rank of T is _______.Correct answer is '2'. Can you explain this answer?

Question

Answer

Here V₃ = V₂ - 2V₁

=> {V₁, V₂} be a L.l. set ⇒ { V₁, V2} be a basis for W => dim W = 2 Now To find Rank T i.e. dim R(T). we firstly find the spanning set for R(T).as

Here {w₁, w₂} be a spanning set for R(T) which is L.l. => if form a basis for R(T) => dim R(T) = 2 = Rank T

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