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1 15 12 3 -12 -15 (a) Find the expansion factor, X₁, that keeps the direction of the vectors in one of the invariant lines of A. The goal of this problem is to find the lines that are invariant under the matrix A = X₁ (b) Find the expansion factor, X₂, that reverses the direction of the vectors in the other invariant line of A. X2 (c) Enter a nonzero vector in the invariant line of A corresponding to the expansion factor in part (a). V1 = V2 M = Σ Note: Your answer should be a vector (v₁, v₂). (d) Enter a nonzero vector in the invariant line of A corresponding to the expansion factor in part (b). M Note: Your answer should be a vector (v₁, v₂). M

1 15 12 3 -12 -15 (a) Find the expansion factor, X₁, that keeps the direction of the vectors in one of the invariant lines of A. The goal of this problem is to find the lines that are invariant under the matrix A = X₁ (b) Find the expansion factor, X₂, that reverses the direction of the vectors in the other invariant line of A. X2 (c) Enter a nonzero vector in the invariant line of A corresponding to the expansion factor in part (a). V1 = V2 M = Σ Note: Your answer should be a vector (v₁, v₂). (d) Enter a nonzero vector in the invariant line of A corresponding to the expansion factor in part (b). M Note: Your answer should be a vector (v₁, v₂). M

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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1 15 12 3 -12 -15 (a) Find the expansion factor, X₁, that keeps the direction of the vectors in one of the invariant lines of A. The goal of this problem is to find the lines that are invariant under the matrix A = X₁ (b) Find the expansion factor, X₂, that reverses the direction of the vectors in the other invariant line of A. X2 (c) Enter a nonzero vector in the invariant line of A corresponding to the expansion factor in part (a). V1 = V2 M = Σ Note: Your answer should be a vector (v₁, v₂). (d) Enter a nonzero vector in the invariant line of A corresponding to the expansion factor in part (b). M Note: Your answer should be a vector (v₁, v₂). M
Transcribed Image Text:1 15 12 3 -12 -15 (a) Find the expansion factor, X₁, that keeps the direction of the vectors in one of the invariant lines of A. The goal of this problem is to find the lines that are invariant under the matrix A = X₁ (b) Find the expansion factor, X₂, that reverses the direction of the vectors in the other invariant line of A. X2 (c) Enter a nonzero vector in the invariant line of A corresponding to the expansion factor in part (a). V1 = V2 M = Σ Note: Your answer should be a vector (v₁, v₂). (d) Enter a nonzero vector in the invariant line of A corresponding to the expansion factor in part (b). M Note: Your answer should be a vector (v₁, v₂). M
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