Q-8 (a) Check whether the following inner product <, > defined by < a, ß > = x1y1 + 2x1Y2 +2x2y1 +5x2Y2, where a = (x1, x2) and ß = (y1, Y2) is an inner product in R2 or not? Justify your answer. (b) Show that the matrix 7 -12 A =|-2 11 -2 10 -2 is diagonalizable. Find the matrix R such that R-AR equals a diagonal matrix D.
Q-8 (a) Check whether the following inner product <, > defined by < a, ß > = x1y1 + 2x1Y2 +2x2y1 +5x2Y2, where a = (x1, x2) and ß = (y1, Y2) is an inner product in R2 or not? Justify your answer. (b) Show that the matrix 7 -12 A =|-2 11 -2 10 -2 is diagonalizable. Find the matrix R such that R-AR equals a diagonal matrix D.
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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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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