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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Q-8 (a) Check whether the following inner product <, > defined by
< a, ß > = x1y1 + 2x1y2 + 2x2y1 + 5x2y2, where a = (x1,x2) and B = (y, Y2)
is an inner product in R2 or not? Justify your answer.
(b) Show that the matrix
7 -12
A =-2 10 -2
7]
-2
is diagonalizable. Find the matrix R such that R-'AR equals a diagonal matrix D.
Transcribed Image Text:Q-8 (a) Check whether the following inner product <, > defined by < a, ß > = x1y1 + 2x1y2 + 2x2y1 + 5x2y2, where a = (x1,x2) and B = (y, Y2) is an inner product in R2 or not? Justify your answer. (b) Show that the matrix 7 -12 A =-2 10 -2 7] -2 is diagonalizable. Find the matrix R such that R-'AR equals a diagonal matrix D.
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