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What is the largest value of the quadratic form $5 x_{1}^{2}-3 x_{2}^{2}$ if $\mathbf{x}^{T} \mathbf{x}=1 ?$

5-3

Algebra

Chapter 7

Symmetric Matrices and Quadratic Forms

Section 2

Quadratic Forms

Introduction to Matrices

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Lectures

01:32

In mathematics, the absolu…

01:11

01:20

What is the largest possib…

01:14

Solve the equation by usin…

01:34

Solve$x^{5}+x^{2} \geq…

03:09

The equation $x^{3}+5 x^{2…

01:01

Solve$x^{2}-x-5 \geq x…

04:51

The maximum value of $y$ f…

00:59

Solve using the Quadratic …

01:29

Which quadratic equation h…

00:55

solve using the quadratic …

01:09

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In mathematics, the absolute value or modulus |x| of a real number x is its …

What is the largest possible value of the quadratic form $5 x_{1}^{2}+8 x_{2…

Solve the equation by using the quadratic formula where appropriate.$$(x…

Solve$x^{5}+x^{2} \geq 2 x^{3}+2$

The equation $x^{3}+5 x^{2}+4=5$ has a solution between $x=0$ and $x=1 .$ Fi…

Solve$x^{2}-x-5 \geq x-2$

The maximum value of $y$ for the quadratic function $f(x)=-x^{2}+x+1$ is 1.<…

Solve using the Quadratic Formula.$5 x^{2}+x=3$

Which quadratic equation has roots $\frac{1}{2}$ and $\frac{1}{3} ?$A. $…

solve using the quadratic formula.$$5 x^{2}+2=2 x$$

Solve the equation by using the quadratic formula where appropriate.$$5 …

02:32

In Exercises $3-6,$ find (a) the maximum value of $Q(x)$ subject to the cons…

03:28

Use the inner product axioms and other results of this section to verify the…

03:14

Exercises $9-14$ require techniques from Section $3.1 .$ Find the characteri…

Compute the quantities in Exercises $1-8$ using the vectors$$\mathbf…

01:58

Use Exercise 19 to show that rank $A^{T} A=$ rank $A .[\text { Hint: How }$ …

03:24

In Exercises 1 and $2,$ find the change of variable $\mathbf{x}=P \mathbf{y}…

03:13

Let $\mathbf{v} \in \mathbb{R}^{n}$ and let $k \in \mathbb{R} .$ Prove that …

07:43

Let $A$ be the matrix of the quadratic form$$9 x_{1}^{2}+7 x_{2}^{2}+11 …

02:15

For the matrices in Exercises $15-17$ , list the eigenvalues, repeated accor…

03:16

In Excrcises $1-6,$ the given set is a basis for a subspace $W .$ Use the Gr…

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