(a) Choose all correct statements: Let S be a linearly independent subset of a vector space R4. If the vector v is in R4, and it is not in S, then the set SU {v} must be linearly independent. Let W be a vector space of dimension 4. A spanning set for W must contain at least 4 vectors. The map F: M33 → M33 defined by F(A) = AB + BA³ , where B = (b) Let T: M22 → R² be the linear map defined by T(X) = X() + X² (₂). where M22 is the set of 2 x 2 real matrices. 551 512) 3 1 1/ 252 , is a linear map. for the domain and (i) Suppose that A is the matrix of the transformation T: M22 → R2 with respect to the standard bases, S₁ = {( ) ( ) ( ) ( )} - {6)·()} S₂ = for the codomain. Find the matrix A and enter your answer, using equation editor, in the box below.

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The intrest on an investment varies directly as the rate of intrest. If the intrest is $53 when thw inntrest rate is 5%, find the intrest when the rate is 3.8%.    The intrest when the rate of intrest is at 3.8% is $_____.