1. Find the LU factorization of the matrix: -3 -7 3369 -9 5 5 20 12...

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1. Find the LU factorization of the matrix: -3 -7 3369 -9 5 5 20 12 122 710 710 2115 -4 -5 Using the LU decomposition find the solution to the system Ax = 2. Consider two points P(4,5) and Q(7,6). Find a. Vector equation of the line L that passes through the points. b. Does the line go through the origin? Justify your answer. 5 7 11 c. Consider the point R(8, 8). Find the projection of the vector PR on the line L. d. Find the distance of R to the line. 3. Suppose u and u are unit vectors in the direction of a and a What is the relation between cosine(a1, a2.) and cosine(u, u)? 1. Find the LU factorization of the matrix: -3 -7 3369 -9 5 5 20 12 122 710 710 2115 -4 -5 Using the LU decomposition find the solution to the system Ax = 2. Consider two points P(4,5) and Q(7,6). Find a. Vector equation of the line L that passes through the points. b. Does the line go through the origin? Justify your answer. 5 7 11 c. Consider the point R(8, 8). Find the projection of the vector PR on the line L. d. Find the distance of R to the line. 3. Suppose u and u are unit vectors in the direction of a and a What is the relation between cosine(a1, a2.) and cosine(u, u)?