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Finding the Inverse of a Linear Transformation In Exercises 31-36, determine whether the linear transformation is invertible. If it is, find its inverse. 31. T(x, y) = (-4x, 4y) 32. T(x, y) = (2x, 0) 33. T(x, y) = (x + y, 3x + 3y) 34. T(x, y) = (x + y, x - y)

Finding the Inverse of a Linear Transformation In Exercises 31-36, determine whether the linear transformation is invertible. If it is, find its inverse. 31. T(x, y) = (-4x, 4y) 32. T(x, y) = (2x, 0) 33. T(x, y) = (x + y, 3x + 3y) 34. T(x, y) = (x + y, x - y)

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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8. Please solve only Question#34
Finding the Inverse of a Linear Transformation In Exercises 31-36, determine whether the linear transformation is invertible. If it is, find its inverse. 31. T(x, y) = (-4x, 4y) 32. T(x, y) = (2x, 0) 33. T(x, y) = (x + 34. T(x, y) = (x + y, 3x + 3y) y₂ x - y) y, 35. T(x₁, x₂, X3) = (x₁, X₁ + X₂, X₁ + x₂ + x3) X2, X1 x2 36. T(X₁, X2, X3, X4) = (x₁ − 2x₂, X₂, X3 + X4, X3)
Transcribed Image Text:Finding the Inverse of a Linear Transformation In Exercises 31-36, determine whether the linear transformation is invertible. If it is, find its inverse. 31. T(x, y) = (-4x, 4y) 32. T(x, y) = (2x, 0) 33. T(x, y) = (x + 34. T(x, y) = (x + y, 3x + 3y) y₂ x - y) y, 35. T(x₁, x₂, X3) = (x₁, X₁ + X₂, X₁ + x₂ + x3) X2, X1 x2 36. T(X₁, X2, X3, X4) = (x₁ − 2x₂, X₂, X3 + X4, X3)
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