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show that T is a linear transformation by finding a matrix that implements the mapping. Note that x₁, x2,... are not vectors but are entries in vector. 17. T(X1, X2, X3, X4) = (0, X₁ + X₂, X₂ + x3, x3 + x4)

show that T is a linear transformation by finding a matrix that implements the mapping. Note that x₁, x2,... are not vectors but are entries in vector. 17. T(X1, X2, X3, X4) = (0, X₁ + X₂, X₂ + x3, x3 + x4)

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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show that T is a linear transformation by finding a matrix that implements the mapping. Note that X₁, X₂, ... are not vectors but are entries in vector. 17. T(X1, X2, X3, X4) = (0, X₁ + X2, X2 + x3, x3 + x4) 19. T(X1, X2, X3) = (x₁ - 5x2 + 4x3, x2 - 6x3) 21. Let T: R² → R2 be a linear transformation such that T(x₁, x₂) = (x₁+x2, 4x₁ + 5x₂). Find x such that T(x) (3,8). =
Transcribed Image Text:show that T is a linear transformation by finding a matrix that implements the mapping. Note that X₁, X₂, ... are not vectors but are entries in vector. 17. T(X1, X2, X3, X4) = (0, X₁ + X2, X2 + x3, x3 + x4) 19. T(X1, X2, X3) = (x₁ - 5x2 + 4x3, x2 - 6x3) 21. Let T: R² → R2 be a linear transformation such that T(x₁, x₂) = (x₁+x2, 4x₁ + 5x₂). Find x such that T(x) (3,8). =
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