Patilputra
The given quadratic form is:
\[
Q(x, y, z) = -x^2 + y^2 + z^2 + 4xy + 4xz
\]
To find the orthogonal canonical reduction and principal axes, we follow these steps:
1. Write the quadratic form in matrix notation:
A quadratic form in three variables can be expressed as:
\[
Q(x, y, z) = \begin{bmatrix} x & y & z \end{bmatrix} \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{12} & a_{22} & a_{23} \\ a_{13} & a_{23} & a_{33} \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix}
\]
By comparing the given form with the general expression, we identify the coefficients of the quadratic form:
\[
Q(x, y, z) = -x^2 + y^2 + z^2 + 4xy + 4xz
\]
The corresponding ___ ________ _______ ____ ______ _________ ____ __________.
_______ ____ _________ ______ ____ _____ ______ ______ ___.
____ _______ ____ ___ __________ _______.
____ _____ _______ ______ _____ _____ _______ _________ _________ ____.
_____ _________ ______ _____ _________ ___ ______ ______.
_______ ________ __________ ____ ________ _______ ___.
____ _____ ___ __________ _____ __________.
_______ ______ _________ ____ __________.
_________ _____ _________ ___ ______ ____ ________ _____ ______ ______ ___ ______.
_____ _________ ___ _____ _________ _____ ___.
______ _____ ___ ___ _________ _________ ______ __________ ________.
________ _____ ____ _____ ______ __________ ________ __________ _________ ___.
_______ _______ ______ ___ ________ ________ _______ _________ __________ _________.
______ _____ _________ ______ __________ __________.
______ _______ __________ _________ _____ ___ ____.
__________ ________ _________ _______ __________ _____ ______ __________ _____ __________ ________.
_________ ______ ________ _____ ______ ______ _______ ______.
_____ ______ __________ ____ ____ _________ ________ ___ ______ ___ _________.
______ ____ _______ _______ ____ _______ _________ ________ __________ _________ ____.
________ _____ ___ _________ ________ __________ __________.
____ __________ ____ _________ _______ __________ _______ ___.
__________ _______ _______ _______ _____ ________ _________ ___ ________ ________ _________ ___.
_____ ____ _________ ____ __________ ______ _________ _________.
_____ _______ _______ ________ _____ ___ _____ _________ ______ ____ _________.
________ _____ ________ ___ _____ _______.
__________ _____ __________ _____ _______ _________ __________ _________.
___ ____ ______ __________ _________ _____.
______ ___ _________ __________ ____ _____ ___ _______ _______ ____ _______.
_________ ________ __________ ________ _______ ______ _________ ______.
_____ ______ __________ ___ _______.
____ __________ _________ _____ _______ ___ ________ ________ ______.
_____ _______ _____ __________ __________ _____ ______ __________.
________ ______ _______ _____ ____.
___ ____ _____ ______ ________ ____ _______ _______ _______.
________ _____ ________ ___ _________ _________ _______ _____.
________ ___ _______ _______ ___.
__________ _____ _____ _____ _________.
______ ______ __________ _______ __________.
___ ______ ___ ______ __________ __________ _____ _____ ______ ___ ___ _____.
_________ ___ _____ ___ _______ ________ __________ _________ _____ ___ _________ _____.
__________ __________ ______ _________ _________ _________ _________ ____ ___ _____.
___ ____ ____ _______ __________ _______ ______ _______.
_____ ______ ________ ____ ______ _____ __________ ______ _______ _____.
_________ ________ _______ _________ _______ ______.
_______ _________ ________ _______ _______.
______ _________ ________ __________ __________.
__________ _____ _______ _____ ___ ________ ___ _____.
___ _________ _________ ___ _____ _______ __________ _______ ____ ________.
_________ __________ _____ ___ ____ ________ ______.
_____ _________ _________ __________ ________ _________.
________ ______ __________ ____ ____ ______ _______ _______ _______ _________ ______.
___ ___ ________ __________ ________ ________ ___ __________ ______.
_____ _________ ______ _____ _______.
______ _______ _______ _________ __________ _______.
Get Full Answer on WhatsApp