The linear transformation T: R → RM is defined by T(v) = Av, where A is as follows.A =0 1-3 1-1 7 7 00 1 8 1(a) Find T(1, 3, 0, 2).STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 0, 2).T(1, 3, 0, 2) =STEP 2: Use your result from Step 1 to solve for T(1, 3, 0, 2).T(1, 3, 0, 2) =0000 (b) Find the preimage of (0, 0, 0).STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation.T(w, x, y, z) =W =X =y =0 1 -3 1-1 7 7 0018 1z = tWLet t be any real number. Set z = t and solve for w, x, and y in terms of t.XZ0STEP 2: Use your result from Step 1 to find the preimage of (0, 0, 0). (Enter each vector as a comma-separated list of its components.)The preimage is given by the set of vectors {(): t is any real number}.

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The linear transformation T: R → RM is defined by T(v) = Av, where A is as follows. A = 0 1-3 1 -1 7 70 0 1 8 1 (a) Find T(1, 3, 0, 2). STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 0, 2). T(1, 3, 0, 2) = 100 STEP 2: Use your result from Step 1 to solve for T(1, 3, 0, 2). T(1, 3, 0, 2) = 000 000 100

The linear transformation T: R → RM is defined by T(v) = Av, where A is as follows. A = 0 1-3 1 -1 7 70 0 1 8 1 (a) Find T(1, 3, 0, 2). STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 0, 2). T(1, 3, 0, 2) = 100 STEP 2: Use your result from Step 1 to solve for T(1, 3, 0, 2). T(1, 3, 0, 2) = 000 000 100

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 12CM

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