Results 1 to 3 of 3

Math Help - Linear Combinations question

  1. #1
    Junior Member
    Joined
    Nov 2008
    From
    Vermont, New England, USA, North America, Earth, Sol Solar System, Orion Arm, Milky Way Galaxy
    Posts
    61

    Linear Combinations question

    I just don't understand what they're asking for/what a combination is...

    Explain why the system
    u+ v+ w=2
    u+2v+3w=1
    v+2w=0
    is singular by finding a combination of the three equations that adds up to 0=1. What value should replace the 0 on the right of the 3rd equation to allow the system to have solutions...what is one solution?

    Write the system in a column picture. Show that the three columns on the left lie in the same plane by expressing the third column as a combination of the first two. WHat are all the solutions (u,v,w) if the column on the right side of the equation is changed to (0,0,0)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,415
    Thanks
    1853

    Re: Linear Combinations question

    Quote Originally Posted by jahichuanna View Post
    I just don't understand what they're asking for/what a combination is...

    Explain why the system
    u+ v+ w=2
    u+2v+3w=1
    v+2w=0
    is singular by finding a combination of the three equations that adds up to 0=1. What value should replace the 0 on the right of the 3rd equation to allow the system to have solutions...what is one solution?
    A "linear combination" of objects x, y, z (vectors, equations, or anything you can add and multiply by numbers) is ax+ by+ cy where a, b, and c are numbers. You are asked to find three numbers a, b, and c, such that a(u+ v+ w)+ b(u+ 2v+ 3w)+ c(v+ 2w)= 0. Of course, you would do the same on the right and have 0= 2a+ b. The problem is telling you that you should find that 2a+ b= 1. If you were to replace that 0 with x, then you would have 2a+ b+ cx. What should x be so 2a+ b+ cx= 0?

    Write the system in a column picture. Show that the three columns on the left lie in the same plane by expressing the third column as a combination of the first two. WHat are all the solutions (u,v,w) if the column on the right side of the equation is changed to (0,0,0)?
    Again, a linear combination is simply sums of numbers times the objects, in this case the columns of the matrix. That is, if the matrix is
    \begin{bmatrix}a & b & c \\ d & e & f\\ g & h & i\end{bmatrix}
    then a "linear combination" of the columns are
    x\begin{bmatrix}a \\ d \\ g\end{bmatrix}+ y\begin{bmatrix}b \\ e \\ h\end{bmatrix}+ z\begin{bmatrix}c \\ f \\ i\end{bmatrix}
    for number x, y, and z.

    I am concerned about your apparent ignorance of basic definitions. Whoever gave you these exercises clearly expects you to know what a "linear combination" is!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2008
    From
    Vermont, New England, USA, North America, Earth, Sol Solar System, Orion Arm, Milky Way Galaxy
    Posts
    61

    Re: Linear Combinations question

    I realized I knew what it was...I just didn't know it by that name...I'm not sure why I hadn't heard of it, but I'll be sure to start reading up on my definitions! Thanks for your help! I got it all done
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. linear combinations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 12th 2011, 02:53 PM
  2. [SOLVED] Linear combinations
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 22nd 2010, 08:34 AM
  3. Column Space and Linear Combinations Question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: June 4th 2009, 08:34 PM
  4. Linear Combinations (Probability) question
    Posted in the Statistics Forum
    Replies: 3
    Last Post: September 29th 2008, 01:53 PM
  5. Replies: 1
    Last Post: November 7th 2006, 08:53 AM

Search Tags


/mathhelpforum @mathhelpforum