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Find the matrix of the quadratic form. Assume $\mathbf{x}$ is in $\mathbb{R}^{3}$ .a. $3 x_{1}^{2}+2 x_{2}^{2}-5 x_{3}^{2}-6 x_{1} x_{2}+8 x_{1} x_{3}-4 x_{2} x_{3}$b. $6 x_{1} x_{2}+4 x_{1} x_{3}-10 x_{2} x_{3}$

a. $A=\left[\begin{array}{ccc}{3} & {-3} & {4} \\ {-3} & {2} & {-2} \\ {4} & {-2} & {-5}\end{array}\right]$b. $A=\left[\begin{array}{ccc}{0} & {3} & {2} \\ {3} & {0} & {-5} \\ {2} & {-5} & {0}\end{array}\right]$

Algebra

Chapter 7

Symmetric Matrices and Quadratic Forms

Section 2

Quadratic Forms

Introduction to Matrices

McMaster University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

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06:47

Find the matrix of the qua…

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Solving a Matrix Equation …

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01:14

01:10

05:04

Use the determinant to dec…

Okay, So for this program, we are even Ah ah, Polly nominal And want to recover the symmetric metrics in this quadratic form. So Patty we have three x one squared plus two x two square minus five x three square minus six x one x two Class Age eggs one x three minus four x two x three So it has three variables. That means we are looking for a three by three matrix. So for a diagonal entrance, So the one y entrant will be the coefficient off excellent squares with three and the two to Incheon will be the coefficient off X two squares. It's too, um, the 33 in trim. It would be like coefficient in front off X three squares. It's minus five for the off diagonal part. Um, so excellent X to a corresponding to this one to Incheon. So we have minus three minus three and the four x one x three. It corresponds to the wife the re engine. So you will be four on the floor and for the last one you will be the 23 entrance. So we have minus two minus two here. And if we told us something for part B. We have the solution. We can directly, right, right out of solution zeros. There, there, since there's no, um, excellent square extra square in the X three square in party and the for the off diagonal parties. 3322 and the minus five minus five.

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