1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: K cannot be what, if you want this matrix to form a basis, confused

  1. Dec 11, 2005 #1
    4 -4 4
    -5 6 -3
    0 4 k
    form a basis for R^3 if and only if k != ?
    since the last col has a k in it, i wanted to see if the first 2 colmuns are linear indepdant, adn they are, becuase i row reduced w/calculator:
    4 -4 0
    -5 6 0
    0 4 0
    and got
    1 0 0
    0 1 0
    0 0 0
    is there a quick way to figure out the k, without mantually row reducing with k? Also if there isn't a quick way, what am i going to be looking for? it will span R^3 if i get
    for the last col with k in it. Thanks.
  2. jcsd
  3. Dec 11, 2005 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    You don't *have* to get down to 1's, merely linearly independent rows/cols, 1s are just nice. And it's better if you say "when do the rows/cols form a basis", rather than "when is the matrix a basis of R^3": the matirx is never a basis of R^3; it isn't even an element of R^3.

    Remember, you're just looking for a solution of Mx=0 to imply x=0, so that's an easy criterion to check when there is only 1 variable (k) to check
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook