Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

Basis for the matrix question.

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Basis for the matrix question.

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

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