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MATH1151 week4c2

# MATH1151 week4c2 - Week 4 Tuesday 10-11 Class Time allowed...

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Time allowed: 15 minutes. 1. (2 marks) Given A = 7 0 1 ,B = 3 3 3 ,C = 4 4 2 , ﬁnd the coordinates of the point D = x y z such that ABCD is a parallelogram. 2. (2 marks) Let A = 6 1 3 = 15 2 6 . Find in parametric vector form the equation of the line through A and B . Is this line parallel to the line ˜ x = 0 12 27 + λ 3 1 1 ? Give a reason for your answer. 3. (3 marks) Let S = ˜ x R 3 : ˜ x = λ 2 1 3 + µ 2 1 1 for 0 λ 2 and λ µ 3 λ Neatly sketch S , labelling all important points. 4. (3 marks) For the following system of equations, write down the corresponding augmented matrix, use Gaussian elimi- nation to transform the augmented matrix into row-echelon form, and solve the system of equations, writing your answer in vector form.

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MATH1151 week4c2 - Week 4 Tuesday 10-11 Class Time allowed...

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