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3. Define the following formal linear transformations... A: R' > R' = A(x, y, z) = (x+y+z, x-2y, y+2z) B: R' → R = B(x, y, z) = (2x +2z, x-y) C: R > R = C(x, y) = (-2x +2y, -3x-y) D: R →R' = D(x, y) = (x+y, y, -x) a. Write the matrices which represent each of the four linear transformations above. b. Write the matrix which represents the transform E = BD.

3. Define the following formal linear transformations... A: R' > R' = A(x, y, z) = (x+y+z, x-2y, y+2z) B: R' → R = B(x, y, z) = (2x +2z, x-y) C: R > R = C(x, y) = (-2x +2y, -3x-y) D: R →R' = D(x, y) = (x+y, y, -x) a. Write the matrices which represent each of the four linear transformations above. b. Write the matrix which represents the transform E = BD.

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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3. Define the following formal linear transformations... A: R' → R' = A(x, y, z) = (x+y+z, x-2y, y+2z) B: R' > R = B(x, y, z) = (2x +2z, x-y) C: R' → R = C(x, y) = (-2x +2y, -3x-y) D: R' → R' = D(x, y) = (x+y, y, –x) a. Write the matrices which represent each of the four linear transformations above. b. Write the matrix which represents the transform E = BD.
Transcribed Image Text:3. Define the following formal linear transformations... A: R' → R' = A(x, y, z) = (x+y+z, x-2y, y+2z) B: R' > R = B(x, y, z) = (2x +2z, x-y) C: R' → R = C(x, y) = (-2x +2y, -3x-y) D: R' → R' = D(x, y) = (x+y, y, –x) a. Write the matrices which represent each of the four linear transformations above. b. Write the matrix which represents the transform E = BD.
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