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H2 Problems 1. Exercise 2.5.14 While trying to invert A, [A I] is carried to [P Q] by row operations. Show that P = QA. 2. Exercise 2.6.23 If x + 0 and y are vectors in R", then show there is a linear transformation T : R" → R" such that T(x) = y. 3. Exercise 3.1.26 Show that the line through two distinct points (x1, yı) and (x2, y2) in the plane has equation 1 X1 1 = 0, |x2 y2 1 4. Exercise 3.2.18 Let A and B be invertible n x n matrices. Show that det(A) = det( B) if and only if A =UB where U is a n x n matrix such that det(U) = 1.

H2 Problems 1. Exercise 2.5.14 While trying to invert A, [A I] is carried to [P Q] by row operations. Show that P = QA. 2. Exercise 2.6.23 If x + 0 and y are vectors in R", then show there is a linear transformation T : R" → R" such that T(x) = y. 3. Exercise 3.1.26 Show that the line through two distinct points (x1, yı) and (x2, y2) in the plane has equation 1 X1 1 = 0, |x2 y2 1 4. Exercise 3.2.18 Let A and B be invertible n x n matrices. Show that det(A) = det( B) if and only if A =UB where U is a n x n matrix such that det(U) = 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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H2 Problems 1. Exercise 2.5.14 While trying to invert A, [A I] is carried to [P Q] by row operations. Show that P = QA. 2. Exercise 2.6.23 If x + 0 and y are vectors in R", then show there is a linear transformation T : R" → R" such that T(x) = y. 3. Exercise 3.1.26 Show that the line through two distinct points (x1, y1) and (x2, y2) in the plane has equation y 1 X1 1 = 0. X2 y2 1 4. Exercise 3.2.18 Let A and B be invertible n x n matrices. Show that det(A) = det(B) if and only if A = UB where U is a n x n matrix such that det(U) = 1.
Transcribed Image Text:H2 Problems 1. Exercise 2.5.14 While trying to invert A, [A I] is carried to [P Q] by row operations. Show that P = QA. 2. Exercise 2.6.23 If x + 0 and y are vectors in R", then show there is a linear transformation T : R" → R" such that T(x) = y. 3. Exercise 3.1.26 Show that the line through two distinct points (x1, y1) and (x2, y2) in the plane has equation y 1 X1 1 = 0. X2 y2 1 4. Exercise 3.2.18 Let A and B be invertible n x n matrices. Show that det(A) = det(B) if and only if A = UB where U is a n x n matrix such that det(U) = 1.
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