Results 1 to 2 of 2

Thread: Linear systems

  1. #1
    Super Member Showcase_22's Avatar
    Sep 2006
    The raggedy edge.

    Linear systems

    The linear system in x,y:

    (1+\lambda)x-\mu y=\delta

    (1-\lambda)x+ \mu y=2

    has a unique solution precisely when:

    a). \lambda=\pm \mu \delta
    b). \mu \neq \delta
    c). \lambda \mu =2\delta
    d). \mu \neq \delta
    What I did:

    \begin{pmatrix}<br />
{1+\lambda}&{-\mu}\\ <br />
{1-\lambda}&{\mu}<br />
\end{pmatrix}\begin{pmatrix}<br />
{x}\\ <br />
{y}<br />
\end{pmatrix}=\begin{pmatrix}<br />
{\delta}\\ <br />
{2}<br />

    The determinant of the matrix cannot be zero so:

    \mu+\mu \lambda+\mu -\mu \lambda=2 \mu

    Hence the answer is d).
    I have a nagging feling about that \delta though....

    Let T_1, T_2, T _3 : \Re^3 \rightarrow \Re ^2 be given by:


    which of T_1,T_2 and T_3 is a linear transformation?

    a). T_1
    b). T_2
    c). T_3
    d). none of them
    I know that for a transformation to be linear:


    applying these, T_2 is the only linear transformation so the answer is b).

    Can someone check these answers?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Apr 2005
    A matrix equation Ax= b has a unique solution if and only if det(A) is not 0. That has nothing to do with the right hand side and so nothing to do with \delta. The right hand side, and \delta, would be important if they asked whether there were no solutions or an infinite number of solutions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Feb 13th 2011, 12:40 PM
  2. Linear Systems Help
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Sep 21st 2010, 08:35 PM
  3. Linear Systems
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: Apr 20th 2010, 04:28 AM
  4. Replies: 7
    Last Post: Aug 30th 2009, 11:03 AM
  5. Linear Systems
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Dec 6th 2007, 02:04 PM

Search Tags

/mathhelpforum @mathhelpforum