Question

Or
4.
Reduce the quadratic form 2x² + 2y2 + 2z2 – 2xy + 2zx-2yz to orthogonal (15M
transformation. Also find signature and rank of the quadratic form.​

Answer 1

Answer:

please write proper question

Step-by-step explanation:

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Answer 2

Answer:

A polynomial with all terms of degree two is known as a quadratic form in mathematics is a quadratic form, for instance, in the variables x and y.

Step-by-step explanation:

What is meant by quadratic form?

A polynomial with all terms of degree two is known as a quadratic form in mathematics ("form" is another name for a homogeneous polynomial). is a quadratic form, for instance, in the variables x and y.

The quadratic formula is a formula that gives the solution(s) to a quadratic equation in elementary algebra. Instead of utilising the quadratic formula, there are alternative methods that include factoring (direct factoring, grouping, AC technique), completing the square, graphing, and others.

Let the equation be $x^2+y^2+z^2-2 x y-2 x z-2 y z=p^{\top} \cdot M \cdot p$

where $p=(x, y, z)^{\top}$ and $M=\left(\begin{array}{ccc}1 & -1 & -1 \\-1 & 1 & -1 \\-1 & -1 & 1\end{array}\right)$

Now solving $M p=\lambda p$ we obtain the eigenvalues and the eigenvectors

$V=\left(\begin{array}{ccc}-1 & 0 & 1 \\-1 & 1 & 0 \\1 & 1 & 1\end{array}\right)$ and then

$M_c=V \cdot M \cdot V^{-1}=\left(\begin{array}{ccc}2 & 0 & 0 \\0 & 2 & 0 \\0 & 0 & -1\end{array}\right)$

The complete question is:

Find the orthogonal canonical reduction of the quadratic form

$x^2+y^2+z^2-2 x y-2 x z-2 y z$. Also find its principal axes?

To learn more about  quadratic form refer to:

https://brainly.in/question/22118085

https://brainly.in/question/49761801

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