Reduce the matrix of the quadratic form $6x_{1}^2 + 3x_{2}^2 + 14x_{3}^2 + 4x_{1}x_{2} + 18x_{1}x{3} + 4x_{2}x_{3}$ to canonical form by congruent transformation and find rank, signature, value class.

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written 9.4 years ago by

teamques10 ★ 70k

modified 3.6 years ago by

saishvilankar793 • 30

Mumbai University > Electronics and Telecommunication > Sem 4 > Applied Maths 4

Marks: 8M

Year: May 2015

engineering mathematics

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written 9.4 years ago by

teamques10 ★ 70k

The quadratic form can be written as

$\begin{bmatrix} a & h & g \\ h & b & b \\ g & b & c \end{bmatrix}$

Comparing given equation with

$a_{11}^2 x_{1}^2 + a_{22}^2 x_{2}^2 + a_{33}^2 x_{3}^2 + 2a_{12} x_{1}x_{2} + 2a_{13}x_{1}x_{3} + 2a_{23}x_{2}x_{3} \\ \therefore A = \begin{bmatrix} …

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