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- Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.In Exercises 1 and 2, determine whether the function is a linear transformation. T:M2,2R, T(A)=|A+AT|Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
- Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.Let T be a linear transformation from R2 into R2 such that T(1,0)=(1,1) and T(0,1)=(1,1). Find T(1,4) and T(2,1).Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3. Find T(0,1,1)
- In Exercises 1-12, determine whether T is a linear transformation. 8. defined byLet T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a the kernel of T and b the range of T. c Determine the rank and nullity of T.In Exercises 1-12, determine whether T is a linear transformation. T:FF defined by T(f)=f(x2)
