A community for students.
Here's the question you clicked on:
 0 viewing
seidi.yamauti
 2 years ago
[linear algebra] <(x1,x2),(y1,y2)> = x1y1 + tx2y2
For which valor of t, it is an in internal (scalar) product?
seidi.yamauti
 2 years ago
[linear algebra] <(x1,x2),(y1,y2)> = x1y1 + tx2y2 For which valor of t, it is an in internal (scalar) product?

This Question is Closed

Traxter
 2 years ago
Best ResponseYou've already chosen the best response.0The internal product (i.e. dot product) of \[\left(\begin{matrix}x1 \\ y1\end{matrix}\right)\] with \[\left(\begin{matrix}x2 \\ y2\end{matrix}\right)\] is \[\left(\begin{matrix}x1+x2 \\ y1+y2\end{matrix}\right)\] So the only value of t which gives this is t=1

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0u have to check one by one the properties of an inner product: (assuming an vector space over \(\mathbb{R}\)) \[ \large \langle a,b\rangle=\langle b,a\rangle \] \[ \large \langle a,b+c\rangle=\langle a,b\rangle+\langle a,c\rangle \] \[ \large \langle\alpha a,b\rangle=\langle a,\alpha b\rangle=\alpha\langle a,b\rangle \] \[ \large \langle a,a\rangle\geq0\quad\text{and}\quad \langle a,a\rangle=0\Leftrightarrow a=0 \]

Traxter
 2 years ago
Best ResponseYou've already chosen the best response.0Ok so I guess inner product isn't just another name you're using for dot product then?

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0that is not true. u can write: \[ \large \langle a,b\rangle=(a_1\quad a_2)\begin{pmatrix} 1 & 0\\ 0 & t \end{pmatrix} \binom{b_1}{b_2} \]

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0\[ \large =a_1b_1+ta_2b_2 \]

seidi.yamauti
 2 years ago
Best ResponseYou've already chosen the best response.0The determinant must be > 0, right? Wich would give the answer t>0. I didn't learn all this procces (I don't really know why, but my teacher didn't explicitly show this transformation of scalar product into matrices product). How I solve by the properties?

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0not the determinant!! for example u might have the matrix \[ \large \begin{pmatrix} 1 & 0\\ 0 & 1 \end{pmatrix} \] has determinant >0 but the resulting expresion is NOT an inner product.

seidi.yamauti
 2 years ago
Best ResponseYou've already chosen the best response.0I see. I'm gonna study more of Linear Algebra, for I don't want to ask you to teach me everything about it hahaha. Thank you very much ;)

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0i think it is a terrific idea. i recomend any of Strang's linear algebra books. there are just great. also hoffman & kunze's

seidi.yamauti
 2 years ago
Best ResponseYou've already chosen the best response.0This Strang is from Gilbert Strang?

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0yes. the one and only

seidi.yamauti
 2 years ago
Best ResponseYou've already chosen the best response.0Understood! Thanks again.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.