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(1) If P = (p1, P2), Q = (q1, 42) and R = (r1, r2) are noncollinear, Pi qi ri then show that A = is invertible. P2 42 r2 1 1 1

(1) If P = (p1, P2), Q = (q1, 42) and R = (r1, r2) are noncollinear, Pi qi ri then show that A = is invertible. P2 42 r2 1 1 1

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) If P = (p1, P2), Q = (q1, 42) and R = (r1, r2) are noncollinear, Pi qi ri P2 92 r2 1 %3D then show that A = is invertible. 1 1 (2) Let a, b, and c be three numbers, not all zero. Show that the set of all points whose barycentric coordinates A, u, and v that satisfy al + bµ + cv = 0 is a line.
Transcribed Image Text:(1) If P = (p1, P2), Q = (q1, 42) and R = (r1, r2) are noncollinear, Pi qi ri P2 92 r2 1 %3D then show that A = is invertible. 1 1 (2) Let a, b, and c be three numbers, not all zero. Show that the set of all points whose barycentric coordinates A, u, and v that satisfy al + bµ + cv = 0 is a line.
Let a, b, and c be three numbers, not all zero. Show that the set of all points whose barycentric coordinates A, µ, and v that satisfy al + bụ + cv = 0 is a line. Let A and B be distinct points of S?. Show that {X € S*|d(X, A) = d(X, B)} is a line, and find and expression for its pole.
Transcribed Image Text:Let a, b, and c be three numbers, not all zero. Show that the set of all points whose barycentric coordinates A, µ, and v that satisfy al + bụ + cv = 0 is a line. Let A and B be distinct points of S?. Show that {X € S*|d(X, A) = d(X, B)} is a line, and find and expression for its pole.
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