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I'm given 4 vectors: $u_1, u_2, u_3$ and $u_4$. I'm going to type them in as points, because it will be easier to read, but think as them as column vectors.

$$u_1 =( 5, λ, λ, λ), \hspace{10pt} u_2 =( λ, 5, λ, λ), \hspace{10pt} u_3 =( λ, λ, 5, λ), \hspace{10pt}u_4 =( λ, λ, λ, 5)$$

The task is to calculate the value of λ if the vectors where linearly dependent, as well as linearly independent.

I managed to figure out that I could put them in a matrix, let's call it $A$, and set $det(A) = 0$ if the vectors should be linearly dependent, and $det(A) \neq 0$ if the vectors should be linearly independent.

Some help to put me in the right direction would be great!

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    Compute the determinant to get a polynomial in the variable $\lambda$; find out for what $\lambda$'s the polynomial is zero vs. nonzero (corresponding to linearly dependent and independent respectively).2012-09-26
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    @anon: That's a lot more effort than is required.2012-09-26

5 Answers 5