Results 1 to 5 of 5

Math Help - 2 short problems

  1. #1
    Junior Member
    Joined
    Mar 2009
    From
    Berkeley, California
    Posts
    26

    2 short problems

    Hi, it's been awhile since I've been on here but I've now officially started Linear Algebra.

    There are two problems in my homework I cannot solve. They are the following:


    1. Find the equation of the form y = mx + b that passes through points (4, -1) and (1,8) using elementary row operations on a matrix.


    2. Find the equation of the parabola y = ax^2 + bx + c that pass through (0,3), (1,9) and (2,3) using elementary row operations on a matrix.


    I believe I have the second problem solved but I am unsure of my answer. Thank you for looking at this! =)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Matt Westwood's Avatar
    Joined
    Jul 2008
    From
    Reading, UK
    Posts
    824
    Thanks
    33
    Show us how you've done the second one and we'll comment.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2009
    From
    Berkeley, California
    Posts
    26
    Actually, I think I may be on my way to answering them both. It's just that I don't know what to do when I get to a certain point. Here goes:

    for the y = mx + b problem....

    I set it up as -1 = m(4) + b and 8 = m(1) + b.

    I set up a matrix that looks like:

    4 1 -1
    1 1 8

    I then set it up in rref form using about 8 steps, until I come out to a matrix that looks like...

    1 0 -3
    0 1 11

    However, I don't really know what this tells me. I don't know how to check it, or set it up in an equation form. I get to the same point in the quadratic problem.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,400
    Thanks
    1848
    Quote Originally Posted by TheBerkeleyBoss View Post
    Actually, I think I may be on my way to answering them both. It's just that I don't know what to do when I get to a certain point. Here goes:

    for the y = mx + b problem....

    I set it up as -1 = m(4) + b and 8 = m(1) + b.

    I set up a matrix that looks like:

    4 1 -1
    1 1 8

    I then set it up in rref form using about 8 steps, until I come out to a matrix that looks like...

    1 0 -3
    0 1 11

    However, I don't really know what this tells me. I don't know how to check it, or set it up in an equation form. I get to the same point in the quadratic problem.
    The whole point of row reduction is that you have transformed the equations 4m+ b= -1 and m+ b= 8 into 1m+ 0b= m= -3 and 0m+ 1b= b= 11. Now, what do you think the equation y= mx+ b is?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2009
    From
    Berkeley, California
    Posts
    26
    Thank you HallsOfIvy. I was able to figure it out from there. I want to understand why this works. Why exactly does rref form work the way it does? I really want to conceptually understand this. What is going on at a geometric level?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. short question :)
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 21st 2010, 01:12 AM
  2. help with short proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 16th 2010, 01:56 PM
  3. A few Short Calculus Practice Problems- HELP!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 11th 2008, 04:16 PM
  4. 2 short calc problems
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 20th 2006, 07:08 PM
  5. not so very short demo of LFT ?
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 26th 2006, 02:52 AM

Search Tags


/mathhelpforum @mathhelpforum