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The linear transformation T: R→ Rm is defined by T(v) = Av, where A is as follows. A = 01 -8 1 -16 30 0 1 51 (a) Find T(1, 3, 2, 0). STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 2, 0). T(1, 3, 2, 0) = STEP 2: Use your result from Step 1 to solve for T(1, 3, 2, 0). T(1, 3, 2, 0) = (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 3.5 1 W []

The linear transformation T: R→ Rm is defined by T(v) = Av, where A is as follows. A = 01 -8 1 -16 30 0 1 51 (a) Find T(1, 3, 2, 0). STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 2, 0). T(1, 3, 2, 0) = STEP 2: Use your result from Step 1 to solve for T(1, 3, 2, 0). T(1, 3, 2, 0) = (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 3.5 1 W []

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The linear transformation T: R" → RM is defined by T(v) = Av, where A is as follows. A = 0 1 -8 1 -1 6 3 0 0 1 5 1 (a) Find T(1, 3, 2, 0). STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 2, 0). T(1, 3, 2, 0) = STEP 2: Use your result from Step 1 to solve for T(1, 3, 2, 0). 4683 T(1, 3, 2, 0) = (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 = 000 X = y = z = t 0 1 8 1 -1 6 30 01 5 1 W X y Z = Lett be any real number. Set z = t and solve for w, x, and y in terms of t. 0 0 0 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. A = 0 1 -8 1 -1 6 3 0 0 1 5 1 (a) Find T(1, 3, 2, 0). STEP 1: Use the definition of T to write a matrix equation for T(1, 3, 2, 0). T(1, 3, 2, 0) = STEP 2: Use your result from Step 1 to solve for T(1, 3, 2, 0). 4683 T(1, 3, 2, 0) = (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 = 000 X = y = z = t 0 1 8 1 -1 6 30 01 5 1 W X y Z = Lett be any real number. Set z = t and solve for w, x, and y in terms of t. 0 0 0 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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