Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**mrpace****Member**- Registered: 2012-08-16
- Posts: 74

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.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,948

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

Offline

Pages: **1**