Answered: Consider the mapping p : R3 → R³…

Consider the mapping p : R3 → R³ defined by p(x1, X2, X3) = (xı + x2, 0, x2 – x3). (a) Show that p is a linear transformation. (b) Find basis for Kernel of p. (c) Find basis for Range of p.

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

Consider the mapping p : R3 → R³ defined by
p(x1, X2, X3) = (xı + x2, 0, x2 – x3).
(a) Show that p is a linear transformation.
(b) Find basis for Kernel of p.
(c) Find basis for Range of p.

Expert Solution

Step 1

According to the given information,

Consider a mapping:

Step 2

For part (a) it is required to show that:

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