Answered: 5. Consider the mapping y : R3 to R3 de…

5. Consider the mapping y : R3 to R3 denfied by (X1,X2,X3) = (X1 + X2,0,X2 - X3). (a) Show that y is a linear transformation. (b) Find basis for Kernel of y. (c) Find basis for Range of y.

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 16CM

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Question

5. Consider the mapping y : R3 to R3 denfied by
(X1,X2,X3) = (X1 + X2,0,X2 - X3).
(a) Show that y is a linear transformation.
(b) Find basis for Kernel of y.
(c) Find basis for Range of y.

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5. Consider the mapping y : R3 to R3 de nfied by (X1,X2,X3) = (X1 + X2,0,X2 - X3). (a) Show that y is a linear transformation. (b) Find basis for Kernel of y. (c) Find basis for Range of y.

5. Consider the mapping y : R3 to R3 denfied by (X1,X2,X3) = (X1 + X2,0,X2 - X3). (a) Show that y is a linear transformation. (b) Find basis for Kernel of y. (c) Find basis for Range of y.