Question

Write the matrix of the quadratic form 2x^2+8z^2+4xy+10xz-2yz. *​

Answer 1

Given: $2x^{2} + 8z^{2} +$ 4xy + 10xz -2yz

To Find: Matrix form of the given Quadratic form

Step-by-step explanation:

q = $2x^{2} + 8z^{2} +$ 4xy + 10xz -2yz

Here, q is the quadratic form in variables x, y, z

The matrix for q :

      A= $\left[\begin{array}{ccc}2&\frac{4}{2} &\frac{10}{2} \\\frac{4}{2} &0&\frac{-2}{2} \\\frac{10}{2} &\frac{-2}{2} &8\end{array}\right]$

         = $\left[\begin{array}{ccc}2&2&5\\2&0&-1\\5&-1&8\end{array}\right]$

It's the symmetric matrix A with this connection to q:

q = $x^{T}$x A x x

Answer 2

Step-by-step explanation:

Write the matrix of the quadratic form

2

2 + 8

2 + 4 + 10 − 2