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MATH115MF06N

MATH115MF06N - 1(a(3 marks Find the parametric equations of...

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(a) (3 marks) Find the parametric equations of the line containing the points (1, 2, –1) and (2, 1, 1). (b) (3 marks) Find the equation of the plane perpendicular to the line in part (a), containing the point (1, 2, –1). 2. (a) (4 marks) Find the general solution to the following system 0 2 5 2 2 4 3 2 1 4 3 2 1 = + + + = + x x x x x x x x (b) (2 marks) What is the solution to the associated homogeneous system? 3. (a) (2 marks) Write the system 2 3 11 1 4 = + = + y x y x in the form of a matrix equation b x A r r = . (b) (2 marks) Find 1 A . (c) (2 marks) Use part (b) to solve the system. 4. (4 marks) Find all possible values of k (if any) such that the vectors − 1 1 k and k k 2 are orthogonal. 5. (6 marks) Find the matrix A where ( ) = 1 6 1 0 1 2 0 0 1 2 1 T A I . 6. Let

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MATH115MF06N - 1(a(3 marks Find the parametric equations of...

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