Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

beketso

linear combinations on vectors.help

  • one year ago
  • one year ago

  • This Question is Closed
  1. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    write the matrix\[E= \left[\begin{matrix}3 & 1 \\ 1 & -1\end{matrix}\right]\]

    • one year ago
  2. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    as a linear combination of the matrices \[A=\left[\begin{matrix}1 & 1 \\ 1& 0\end{matrix}\right]\]

    • one year ago
  3. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    \[B=\left[\begin{matrix}0 & 0 \\ 1 & 1\end{matrix}\right]\]

    • one year ago
  4. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    \[C=\left[\begin{matrix}0 & 2 \\ 0 & -1\end{matrix}\right]\]

    • one year ago
  5. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    are there just three?

    • one year ago
  6. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    basically ,you write the matrix E as a linear combination of the matrices A,B, and C

    • one year ago
  7. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    @richyw ,yes there only three

    • one year ago
  8. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    ok so the concepts you need here are matrix addition and scalar multiplication.

    • one year ago
  9. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    you can solve this one in different ways but it's simple enough to do by inspection

    • one year ago
  10. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    so looking at E, the first thing I notice is that \(e_{11}=3\) now looking at matrices A, B, and C. The only one that has anything but 0 in that position is matrix A, so we know already that it must be 3 times matrix A. which gives. \[\left[\begin{matrix}3 & 3 \\ 3 & 0\end{matrix}\right]\] right?

    • one year ago
  11. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    ok i got that part

    • one year ago
  12. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    alright so now look at matrix E and notice that position \(e_{12}\) is 2, so we need to subtract a certain amount from matrix A to produce a 2 there.

    • one year ago
  13. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    well, matrix B has a zero in that position, so it is no good, so subtract one times matrix C from matrix A and we get \[3A-C=\left[\begin{matrix}3&1\\3&1\end{matrix}\right]\]

    • one year ago
  14. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry I should have said "subtract one times matrix C from three times matrix A". Now I hope you can see what multiple of matrix B you bust subtract to get E

    • one year ago
  15. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    are you following?

    • one year ago
  16. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah

    • one year ago
  17. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    alright cool well then you have the answer!

    • one year ago
  18. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    so it is 3A-2B-C=E?

    • one year ago
  19. richyw
    Best Response
    You've already chosen the best response.
    Medals 1

    yes!

    • one year ago
  20. beketso
    Best Response
    You've already chosen the best response.
    Medals 1

    thanx a lot!!!!!!!

    • one year ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.