find an LU factorization of the given matrix.

Calc III Lec Day 1 8/29/16 Ch. 11.2 Vector : a set of ordered numbers Ex) vector a = (1,2,3) which does not equal (2,3,1) Uses 1. Locate points in space a. Vector a = (a ,1 ,2 )3means that from the origin (0,0,0) vector a terminates at point (a ,a1,a2) 3nd starts at point (0,0,0) 2. Vector Operations aka Algebra of Vectors a. Vector a = (a ,1 ,2 )3vector b = (b ,b 1b 2, 3 + b = (a- 1b ,1 +2 ,a2+b3) 3 b. Any number c times a vector a = (ca ,ca ,c1 ) 2 3 c. a + b = b + a 3. Diagonals of a Parallelogram a. For a parallelogram with adjacent sides formed by vectors a and b i. The long diagonal = a + b ii. The short diagonal = a – b 4. Unit Vector a. A vector with length 1 in the direction of vector a = i. This is dividing vector a by its length b. For 3 dimensional Cartesian systems, the unit vectors i, j, and k represent a vector of length 1 along the x, y, and z axis, respectively 5. Equations a. Vector a = (1,2,3) can be written as a = 1i + 2j + 3k b. In 2 dimensions, vector a can be described as where theta is the angle above the x -axis of the vector. Generalized Formulas 1. Length of an n dimensional vector a a. Calc III Lec Day 2 8/31/16 Ch. 11.3 Dot Product Properties 1. Symmetric,