- #1

DoderMan

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a) Find all values of λ E R, such that {u1, u2, u3} spans R3, i.e.R3 = span {u1, u2, u3}

b) Find the value of λ E R, such that {u1, u2, u3} spans a plane in R3.

c) Find all values of k E R, such that the vector v=(8,6,k) belongs to the plane spanned by {u1,u2,u3} (for the value of λ which you obtained in part (b))

In part (a) I took the determinante of the vectors {u1,u2,u3} and I got λ=12. Is the procedure and solution correct?

In part (b) I performed Gauss-jorden elimination method on vectors {u1,u2,u3} and I got λ=6. Is the procedure and solution correct?

In part (c) I again performed Gauss-jorden elimination method on vectors {u1,u2,u3,v} and I found that k= (16/3). Is the procedure and solution correct?

I am also confused about part (a) and (b). In part (a) the three vectors span R3 but in part (b) the three vectors span a plane in R3. How is it possible?

Thanks in advance.