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Elementary Linear Algebra (MindTap Course List)
- Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.arrow_forwardFind the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forwardFind 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.arrow_forward
- In Exercises 1-12, determine whether T is a linear transformation. 5. T:Mnn→ ℝ defined by T(A)=trt(A)arrow_forwardIn Exercises 1 and 2, determine whether the function is a linear transformation. T:M2,2R, T(A)=|A+AT|arrow_forwardIn Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB, where B is a fixed nn matrixarrow_forward
- In Exercises 1-12, determine whether T is a linear transformation. 8. defined byarrow_forwardLet 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)arrow_forwardLet T be a linear transformation from R2 into R2 such that T(1,2)=(1,0) and T(1,1)=(0,1). Find T(2,0) and T(0,3).arrow_forward
- Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and nullity of T. (b) Find a basis for the kernel of T.arrow_forwardLet 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.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning