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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- 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.arrow_forwardLet T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.arrow_forwardIn Exercises 1-12, determine whether T is a linear transformation. 5. T:Mnn→ ℝ defined by T(A)=trt(A)arrow_forward
- In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB, where B is a fixed nn matrixarrow_forwardIn Exercises 1-12, determine whether T is a linear transformation. 8. defined byarrow_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
- In Exercises 1-12, determine whether T is a linear transformation. T:FF defined by T(f)=f(x2)arrow_forwardIn Exercises 1 and 2, determine whether the function is a linear transformation. T:M2,2R, T(A)=|A+AT|arrow_forwardLet 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_forward
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