Reducing Quadratic form

Asked Jan 12 '20 at 09:24

Active Jan 12 '20 at 17:13

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Reduce the quadratic form to a canonical form and find the rank index and signature. Write down the corresponding equations of transformation:

$$ 4x_1^2 + 3x_2^2 - x_3^2 + 2x_2 x_3 - 4x_3 x_1 + 4x_1 x_2 $$

The given solution says:
$(w1)^2 + (w2)^2 - (w3)^2 ;$
$r=3, p=2, s=1;$
$x_1 = (1/2)(w_1) - (\sqrt 2/4)(w_2) + (1/2)(w_3),$
$x_2 = (\sqrt 2/2)(w_2) - (1/2)(w_3),$
$x_3 = (1/2)(w_3)$

Can anyone provide with detailed ans,how they come up with this?

edited Jan 12 '20 at 17:13

hardmath

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asked Jan 12 '20 at 09:24

Syeda Fatima Fayruj

1

What have you tried? Did you already look here at this site, e.g., here, or here etc.? – Dietrich Burde Jan 12 '20 at 09:25
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Jan 12 '20 at 09:27
Despite voting to close your Question as a duplicate, I have improved the formatting to show you how $\LaTeX$ and MarkDown can be used to make such posts more legible. Please review my edit, both to check that I did not unintentionally change your meaning and to gather an idea how to use math notation here in the future. – hardmath Jan 12 '20 at 17:16

Reducing Quadratic form

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