Let Q be the matrix: 1 2 k
0 -1 2
k 2 1
Find all real values of k such that the columns of Q do not form a basis of R3.
My thoughts on this: k appears in the x and z row. It seems to me that the 2 known elements in the x and z row already span the entire xz plane. Therefore I think that any value of k other than zero is the answer but i'm really not confident.
Would appreciate help, thanks.
The third vector must not be a linear combination of the other two. I think that means that the matrix must be non singular. So calculate the determinant and find the values of k so that 'det' is zero.
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