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 ______ __________ ______ ___ __________ ____ ________ ________.
__________ ________ ________ _______ _______ ________ ___ _________ _______ __________ ________ _____.
________ ________ ___ _______ __________ _____ ___ _____ ________.
________ ______ ____ _______ _____.
_____ ___ ______ _________ ___ _____ ____.
____ _________ _____ _____ ______.
______ ____ __________ ___ _________.
_______ ________ _____ _________ ____ ________ ______ ______ ____.
______ ____ _________ _____ _________.
________ ______ ___ _______ ______ ____ _________.
__________ _________ ___ ______ __________.
__________ ____ ________ ______ _____ __________ ______ ____ _________ ___.
___ ___ __________ __________ _____ _______ ___ ___ ___ __________ _________ __________.
__________ _______ __________ ____ _________ ____ _______ _____ _____ _______ ________ __________.
_________ ________ _______ _____ _______ _____ ___ ____ _______ ____.
_____ ________ ________ _________ _______ ___.
_____ __________ __________ ___ _______ _______ _____ ___ _______ __________.
_______ _________ _________ _______ __________ _____ ____ _________ _______ ______ ____.
______ ____ ____ ______ _____ ______ ______ __________ ____ ___ _________.
______ _________ ______ _________ ___ ____.
_____ ________ ________ ______ _____ ________ ____ ________ __________ ________.
_____ __________ _________ _____ ________ _________ ______ ________ ____ _____ _________ ______.
____ ________ __________ _____ _____ _______ ________ ______.
_________ ______ ________ __________ _____ ______ _________.
______ _____ _____ _________ __________ ______ ___ ___ _____ _____ ___ _____.
______ _______ _______ ______ ___ _______ ______.
______ ______ ____ _______ ________ ______ ________ __________.
___ _________ ___ ____ ________ ____ _________ ___ ______ __________ ___ _________.
_____ _______ ___ _________ _______.
_________ _________ ______ __________ _______ ___ ________ _____ ____ _________ ________.
___ _________ _____ _________ ____.
_____ _________ _____ _______ _____ _______ _________ _______.
____ ___ _____ _____ ________ _____ _____ ____ _________ _______ __________ ________.
_________ ______ _________ ___ _________ ____ ____ ____.
_________ ______ _________ _________ _____ _______ _____ _______ _________ _____ ______ ________.
________ ________ _________ ____ _____ _______ _____ ______.
_________ ____ ________ _______ ______.
_______ _________ ________ ____ ___ ____ _______ _________ __________ _________ ____.
________ ________ _______ ________ __________ ___ __________ ____ _____.
_____ __________ __________ ____ ____ _______ ________ ____ ____ _________ _____.
_______ _________ _______ _____ ________ ______ _____ ____ ______ ________ _____ _________.
______ _______ ____ ___ ____ _________.
_____ _________ __________ ___ _________.
_______ ______ _______ ________ ___ _______ __________ ______ _____ ________.
_________ ___ ________ ____ ______.
___ ____ _______ ___ ________ __________ _________ __________.
____ ___ _____ ____ ___ ___ ______ ________ __________ __________ ____.
__________ ____ _________ __________ _________ ________ ___ _______ _______ __________.
___ __________ _________ ________ ________ ________ ___ __________ __________.
______ _____ _________ _________ ________ ________ __________ _______ ______ _________ ___.
______ ______ _____ _______ ____.
___ _________ __________ _____ _____ _______.
_____ ____ _____ _____ ______ ________ ____ _______ _________ _______ ___ __________.
____ ___ ________ _____ _______ ____ ______ _________ __________ ___ ___.
_____ _________ _________ ________ ________ ____ ______ _________ _____.
____ _____ __________ _________ ______ ___ ___ _______.
Get Full Answer on WhatsApp