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MATH1151 week4c1

# MATH1151 week4c1 - Week 4 Monday 12-1 Class Time allowed 15...

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Time allowed: 15 minutes. 1. (2 marks) Suppose ˜ u = 3 4 2 , ˜ v = 2 3 3 , ˜ w = 1 0 0 0 . Calculate ˜ u 4 ˜ v and 13 ˜ u 12 ˜ v + ˜ w if they are defined, or explain why they are not defined. 2. (2 marks) Find the equation of the line through 2 7 4 and parallel to 3 8 1 in vector parametric form. Is the point 2 1 1 on this line? Give a reason for your answer. 3. (3 marks) Find the intersection of the line ˜ x = 3 0 1 + λ 7 1 1 with the plane 3 x 2 y + 5 z = 50. 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. x 2 y + 3 z = 11 x + 2 y + z = 7 4 x 2 y + 6 z = 20 Week 4 Monday 12-1 Class

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