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Question: matrix algebra...

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Matrix algebra

1. 10 Let the vectors (a) 2 Calculate ui-2i (b) 4] Find a unit vector that points in the same direction as 2u--i (c) 4 Find a unit vector y that is perpendicular to both u and . How many such vectors are there? 2. 10 Consider the line that passes through the two points (1,1,1) and (2, 1,0) (a) 5 Find a parametric equation for the line (b) Find its intersection with the plane x-+ x2 + 2x3 = 5. 3. 101 Determine whether the following vectors are linearly dependent Justify your answer (a) The set ( (b) |51 The vectors u, F, and in Question1 4. 10 Determine if the following sets are subspaces of R3. Jstify your answer 0)
5. 1101 (a) 12 Find the plane that passes through the point P-(1,1,1) and is perpendicular to the line (b) 14] Find a point Q on the line L given by the following equation such that the segment PO is perpendicular to the line L (c) |4] Find the number a and a point R on the line such that the segment PR is perpendicular to the plane that you found in part 6 110 Show that the following statements are true for all vectors, in R. (b) 151 If +91|-ll/- 1, then is orthogonal to y.
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