For matrix transformation T(x) = Ax, the rank of transformation T is the same as the rank of matrix A and the nullity of T is the same as the nullity of A. Let T: R → R² be defined by T(x) = Ax where A is given below. 2 A = 4 -2 1 2 0 -2 0 2 -6 -12 -5 7 -5 [0 0 1 1 What is rank(T)? Ex: 5 What is nullity(T)? Ex: 5

For matrix transformation T(x) = Ax, the rank of transformation T is the same as the rank of matrix A and the nullity of T is the same as the nullity of A. Let T: R → R² be defined by T(x) = Ax where A is given below. 2 A = 4 -2 1 2 0 -2 0 2 -6 -12 -5 7 -5 [0 0 1 1 What is rank(T)? Ex: 5 What is nullity(T)? Ex: 5

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

See similar textbooks

Similar questions

Let T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.
In Exercises 3-6, prove that the given transformation is a linear transformation, using the definition (or the Remark following Example 3.55). T[xy]=[yx+2y3x4y]
In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB, where B is a fixed nn matrix
In Exercises 7-10, give a counterexample to show that the given transformation is not a linear transformation. 9.
Let T be a linear transformation from M2,2 into M2,2 such that T([1000])=[1102], T([0100])=[0211], T([0010])=[1201],T([0001])=[3110]. Find T([1314]).
In Exercises 3-6, prove that the given transformation is a linear transformation, using the definition (or the Remark following Example 3.55). 6.
Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
The figure shows three outline versions of the letter F. The second one is obtained from the first by shrinking horizontally by a factor of 0.75, and the third is obtained from the first by shearing horizontally by a factor of 0.25. a Find a data matrix D for the first letter F. b Find a transformation matrix T that transforms the first F into the second. Calculate TD, and verify that this is a data matrix for the second F. c Find the transformation matrix S that transforms the first F into the third. Calculate SD, and verify that this is a data matrix for the third F.
Let 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.