Results 1 to 3 of 3

Thread: 6.1.3-4 Show that the given columns of f(x) are linearly independent on the interva;

  1. #1
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    716
    Thanks
    1

    6.1.3-4 Show that the given columns of f(x) are linearly independent on the interva;

    $\textsf{Show that the given columns of functions are linearly independent on the interval
    $(-\infty,\infty)$}$
    3.
    $$\left[\begin{array}{c}e^{2x}\cos{3x} \\ -e^{2x}\sin{3x} \end{array}\right]
    ,\left[\begin{array}{c}e^{2x}\sin{3x} \\ -e^{2x}\cos{3x} \end{array}\right]$$
    ok clearly new at this but thot to start with
    $$\left[\begin{array}{c}e^{2x}\cos{3x} \\ -e^{2x}\sin{3x} \end{array}\right]
    +\left[\begin{array}{c}e^{2x}\sin{3x} \\ -e^{2x}\cos{3x} \end{array}\right]
    =\left[\begin{array}{c}0 \\ 0 \end{array}\right]$$
    ------------------------------------------------------------------------------
    4.
    $$\left[\begin{array}{c}e^{-2x}\\0\\0 \end{array}\right],
    \left[\begin{array}{c}0\\ 3\cos{5x}\\ -3\sin{3x} \end{array}\right]
    ,\left[\begin{array}{c} 0\\ \sin{3x}\\ \cos{5x} \end{array}\right]$$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Walagaster's Avatar
    Joined
    Apr 2018
    From
    Tempe, AZ
    Posts
    192
    Thanks
    120

    Re: 6.1.3-4 Show that the given columns of f(x) are linearly independent on the inter

    Quote Originally Posted by bigwave View Post
    $\textsf{Show that the given columns of functions are linearly independent on the interval
    $(-\infty,\infty)$}$
    3.
    $$\left[\begin{array}{c}e^{2x}\cos{3x} \\ -e^{2x}\sin{3x} \end{array}\right]
    ,\left[\begin{array}{c}e^{2x}\sin{3x} \\ -e^{2x}\cos{3x} \end{array}\right]$$
    ok clearly new at this but thot to start with
    $$\left[\begin{array}{c}e^{2x}\cos{3x} \\ -e^{2x}\sin{3x} \end{array}\right]
    +\left[\begin{array}{c}e^{2x}\sin{3x} \\ -e^{2x}\cos{3x} \end{array}\right]
    =\left[\begin{array}{c}0 \\ 0 \end{array}\right]$$
    ------------------------------------------------------------------------------
    4.
    $$\left[\begin{array}{c}e^{-2x}\\0\\0 \end{array}\right],
    \left[\begin{array}{c}0\\ 3\cos{5x}\\ -3\sin{3x} \end{array}\right]
    ,\left[\begin{array}{c} 0\\ \sin{3x}\\ \cos{5x} \end{array}\right]$$
    Hint: What happens if you try $x=0$ in those?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    Wahiawa, Hawaii
    Posts
    716
    Thanks
    1

    Re: 6.1.3-4 Show that the given columns of f(x) are linearly independent on the inter

    so for these if x=0 then
    $$\left[\begin{array}{c}1\\0\\0 \end{array}\right],
    \left[\begin{array}{c}0\\ 3\\ 0 \end{array}\right]
    ,\left[\begin{array}{c} 0\\ 0\\ 1 \end{array}\right]$$

    would this rref into
    $$\left[\begin{array}{c}1&0&0\\0&1&0\\0&0&1 \end{array}\right]$$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Show that a set of functions is linearly independent
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Nov 10th 2012, 06:39 AM
  2. Replies: 1
    Last Post: Oct 14th 2012, 07:57 AM
  3. Replies: 1
    Last Post: Mar 9th 2011, 08:42 PM
  4. Replies: 1
    Last Post: Oct 27th 2010, 05:41 AM
  5. Show Linearly Independent
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Oct 18th 2009, 03:19 PM

/mathhelpforum @mathhelpforum