aS FAST as possible please! please provide a typewritten solution i would be grateful! PROBLEM 1 Problem 1. Consider the vectors(0-0-0-0Let {e,, e2, es} be the standard basis in R3 and let T : R³ → R' be the lineartransformation defined byT(e1) = V1, T(e2) = v2, T(e3) = V3.(а) Write down the matrir Ar such that T(x) — Арх.(b) What is the dimension of R(T), the range of T? Is the vector w inR(T)? Justify your answers.(c) State the rank-nullity theorem for linear transformations and use it todetermine the dimension of the null space N(T) of T.(d) Find a basis of N(T).

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Problem 1. Consider the vectors 3 Let {e1, e2, es} be the standard basis in R° and let T : R³ → R* be the linear transformation defined by T(e1) = V1, T(e2) = v2, T(e3) = V3. (a) Write down the matrir Ar such that T(x) = ATX. (b) What is the dimension of R(T), the range of T? Is the vector w in R(T')? Justify your answers. (c) State the rank-nullity theorem for linear transformations and use it to determine the dimension of the null space N(T) of T.

Problem 1. Consider the vectors 3 Let {e1, e2, es} be the standard basis in R° and let T : R³ → R* be the linear transformation defined by T(e1) = V1, T(e2) = v2, T(e3) = V3. (a) Write down the matrir Ar such that T(x) = ATX. (b) What is the dimension of R(T), the range of T? Is the vector w in R(T')? Justify your answers. (c) State the rank-nullity theorem for linear transformations and use it to determine the dimension of the null space N(T) of T.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...

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