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Let T₁ and T₂ be linear transformations from R³ into R³ such that T₁ (X₁, X2, X3) = (X1 + X3, X1 + X2 − X3, X1 − X2 + 3x3) and T₂ (X₁, X2, x3) = (x₁ - 2x3, x1 - x2 - X3, X3 − X1). Find the standard matrix for the composition T = T₂0T₁ (standard matrix of T is the matrix with respect to the standard bases).

Let T₁ and T₂ be linear transformations from R³ into R³ such that T₁ (X₁, X2, X3) = (X1 + X3, X1 + X2 − X3, X1 − X2 + 3x3) and T₂ (X₁, X2, x3) = (x₁ - 2x3, x1 - x2 - X3, X3 − X1). Find the standard matrix for the composition T = T₂0T₁ (standard matrix of T is the matrix with respect to the standard bases).

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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Let T₁ and T₂ be linear transformations from R³ into R³ such that T₁ (X₁, X2, X3) = (X1 + X3, X1 + X2 − X3, X1 − X2 + 3x3) and T₂ (x₁, x2, X3) = (x₁ - 2x3, x1 - x2 - X3, X3 − X1). Find the standard matrix for the composition T = T₂0T₁ (standard matrix of T is the matrix with respect to the standard bases).
Transcribed Image Text:Let T₁ and T₂ be linear transformations from R³ into R³ such that T₁ (X₁, X2, X3) = (X1 + X3, X1 + X2 − X3, X1 − X2 + 3x3) and T₂ (x₁, x2, X3) = (x₁ - 2x3, x1 - x2 - X3, X3 − X1). Find the standard matrix for the composition T = T₂0T₁ (standard matrix of T is the matrix with respect to the standard bases).
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