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The linear transformation T: R Rm is defined by T(v) = Av, where A is as follows. 0 1 -6 1 A = -1 4 2 0 0 1 5 1 (a) Find T(0, 2, 3, 1). STEP 1: Use the definition of T to write a matrix equation for T(0, 2, 3, 1). T(0, 2, 3, 1) = STEP 2: Use your result from Step 1 to solve for T(0, 2, 3, 1). T(0, 2, 3, 1) = (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 1 -6 1 T(w, x, y, z) = -1 4 2 0 y 0 1 5 1 Let t be any real number. Set z = t and solve for w, x, and y in terms of t. W = X = y = z = t STEP 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}.

The linear transformation T: R Rm is defined by T(v) = Av, where A is as follows. 0 1 -6 1 A = -1 4 2 0 0 1 5 1 (a) Find T(0, 2, 3, 1). STEP 1: Use the definition of T to write a matrix equation for T(0, 2, 3, 1). T(0, 2, 3, 1) = STEP 2: Use your result from Step 1 to solve for T(0, 2, 3, 1). T(0, 2, 3, 1) = (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 1 -6 1 T(w, x, y, z) = -1 4 2 0 y 0 1 5 1 Let t be any real number. Set z = t and solve for w, x, and y in terms of t. W = X = y = z = t STEP 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}.

Elementary Linear Algebra (MindTap Course List)
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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The linear transformation T: R" - Rm is defined by T(v) = Av, where A is as follows. 0 1 -6 1 A = -1 4 2 0 0 1 5 1 (a) Find T(0, 2, 3, 1). STEP 1: Use the definition of T to write a matrix equation for T(0, 2, 3, 1). T(о, 2, 3, 1) %3 STEP 2: Use your result from Step 1 to solve for T(0, 2, 3, 1). T(0, 2, 3, 1) = (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 1 -6 1 T(w, x, y, z) = -1 4 2 0 0 1 5 1 Let t be any real number. Set z = t and solve for w, x, and y in terms of t. W = X = y = z = t STEP 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}.
Transcribed Image Text:The linear transformation T: R" - Rm is defined by T(v) = Av, where A is as follows. 0 1 -6 1 A = -1 4 2 0 0 1 5 1 (a) Find T(0, 2, 3, 1). STEP 1: Use the definition of T to write a matrix equation for T(0, 2, 3, 1). T(о, 2, 3, 1) %3 STEP 2: Use your result from Step 1 to solve for T(0, 2, 3, 1). T(0, 2, 3, 1) = (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 1 -6 1 T(w, x, y, z) = -1 4 2 0 0 1 5 1 Let t be any real number. Set z = t and solve for w, x, and y in terms of t. W = X = y = z = t STEP 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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