q3 let u i ii iii iv q s t n p 0 u r and w 1 a calculate the angle bet
Let u =
R and w =
Calculate the angle between the two vectors u and v.
Find the value of a such that u and w are orthogonal.
Find the value of a such that u, v, w are linearly dependent.
State the "Basis Theorem". Choose a value of a, different from the one that you
have found in (iii), so that u, v and w become linearly independent, apply the
"Basis Theorem" to obtain a basis for the three-dimensional space R3 using
Gaussian Elimination Method. Find the coordinates of 3 in terms of this basis.
(Marks will ONLY be awarded for Gaussian Elimination Method.)
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