The vectors
v =
are linearly independent if and only if k does not equal ______?
Ok so i set up the matrix
then i reduced it down to this
Not sure what to do now or if i am even headed in the right direction
Thanks for any suggestions.
The vectors
v =
are linearly independent if and only if k does not equal ______?
Ok so i set up the matrix
then i reduced it down to this
Not sure what to do now or if i am even headed in the right direction
Thanks for any suggestions.
you're almost there! u, v and w are linearly independant when the equation only admits the trivial solution which is when the scalars . you need to find a k such that your system of equations satisfies this condition. this is the same as saying that your matrix can be reduced to a diagonal matrix!
No! First off, you should avoid dividing by an expression containing because the expression might be zero. In any case, I believe you also made a calculation mistake (the numerator of the fraction should be and not ).
When you reach
you can subtract times the second row from the third, to get
No divisions involved!
Now you want the bottom right corner to be nonzero, i.e. you want .
Check to see if you get the same answer with the determinant method. I didn't check all your calculations so I can't guarantee you that your answer is correct!