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389. The triangular region R with the vertices (0, 0), (2, 0), and (1,3) is shown in the following figure. YA 3 2+ 1 0 1 2X a. Find a transformation T: S→ R, T (u, v) = (x, y) = (au + bv, cu + dv), where a, b, c and d are real numbers with ad-bc0 such that T-¹ (0,0) = (0,0), T-¹ (2,0) = (1,0), and T-¹ (1,3)= (0, 1). b. Use the transformation T to find the area A (R) of the region R.

389. The triangular region R with the vertices (0, 0), (2, 0), and (1,3) is shown in the following figure. YA 3 2+ 1 0 1 2X a. Find a transformation T: S→ R, T (u, v) = (x, y) = (au + bv, cu + dv), where a, b, c and d are real numbers with ad-bc0 such that T-¹ (0,0) = (0,0), T-¹ (2,0) = (1,0), and T-¹ (1,3)= (0, 1). b. Use the transformation T to find the area A (R) of the region R.

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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389. The triangular region R with the vertices (0, 0), (2, 0), and (1, 3) is shown in the following figure. YA 3 2+ 1 0 1 2X a. Find a transformation T: S→ R, T (u, v) = (x, y) = (au + bv, cu + dv), where a, b, c and d are real numbers with ad - bc #0 such that T-¹ (0,0) = (0,0), T-¹ (2,0) = (1,0), and T-¹ (1,3) = (0, 1). b. Use the transformation T to find the area A (R) of the region R.
Transcribed Image Text:389. The triangular region R with the vertices (0, 0), (2, 0), and (1, 3) is shown in the following figure. YA 3 2+ 1 0 1 2X a. Find a transformation T: S→ R, T (u, v) = (x, y) = (au + bv, cu + dv), where a, b, c and d are real numbers with ad - bc #0 such that T-¹ (0,0) = (0,0), T-¹ (2,0) = (1,0), and T-¹ (1,3) = (0, 1). b. Use the transformation T to find the area A (R) of the region R.
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