ECE 3043 Lecture Notes - Linear Combination

• School: Georgia Tech
• Department: Electrical & Computer Engr
• Course: ECE 3043
• Professor: Smith

Document Summary

Lectures based on course notes by pablo laguna and kostas. In many instances we need to solve a x = b, where. X = x1 x2 x3 xn b1 b2 b3 bn. The eigenvalues and eigenvectors of a matrix a. Consider a x = b with a a n n matrix with det (a) (cid:54)= 0. We will try to transform it into an upper-triangular linear system. 0 0 1 and compute m1a x = m1b. 0 a22 a21 a11 a32 a31 a11 a12 a12 a13 a23 a21 a11 a33 a31 a11 a13 a13. 0 an2 an1 a11 a12 an3 an1 a11 a13. 0 a32 (1) (1) a13 (1) a23 (1) a33. M1b = b1 b2 a21 a11 b3 a31 a11 bn an1 a11 b1 b1 b1 (1) (1) (1) (1) b1 b2 b3 bn. The procedure can be repited to eliminate now a32 (1)