A community for students.
Here's the question you clicked on:
 0 viewing
rvc
 one year ago
Matrices.
Please help :)
For what value of x will the following matrix A be of rank
1) equal to 3
2) less than 3
rvc
 one year ago
Matrices. Please help :) For what value of x will the following matrix A be of rank 1) equal to 3 2) less than 3

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0where is the matrix?

rvc
 one year ago
Best ResponseYou've already chosen the best response.0\[A=\left[\begin{matrix}3x & 2 & 2 \\ 1 &4x & 0 \\ 2 & 4 & 1x\end{matrix}\right]\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0really, you need to find x so that the determinant is nonzero which will make the matrix have full rank (3). and then find x so that the determinant is 0 then the matrix will not have full rank which means the rank will be less than 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know how to calculate the determinant?

rvc
 one year ago
Best ResponseYou've already chosen the best response.0should i equate the determinant to zero?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0once you get the expression for the determinant, you should have a 3rd degree polynomial. if you find the roots of that polynomial, then when x is the value of anoy of the roots, the determinant will be 0 and the second part of your question will be answered. if you pick any value that is not a root, then the determinant will be nonzero and you will have answered the first part of the question.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you understand? the dots i'm trying to help you connect?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the first part is actually the easier of the two because you can use trial and error and there are an infinite number of values that will work. but for part 2, a maximum of 3 values work, and only one value if the polynomial has a pair of complex roots!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you are doing by hand, you can use the rational roots theorem to find the roots.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did you find the answers?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did you get the polynomial?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did you want help finding the answers?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the rank is 3 when the null space is trivial, i.e. only zero; this means that the entire codomain is mapped to. so we want \(\det A\ne 0\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if the null space is not trivial, then we will invariably have incomplete rank and so for rank less than 3 we want to solve \(\det A=0\)
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.