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**mrpace****Member**- Registered: 2012-08-16
- Posts: 72

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.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

hi mrpace,

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.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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