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homework3
Course: Y 05, Fall 2009School: Virginia Tech
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- Homework3 LU factorization Problem 1: Consider a gaussian elimination performed on a 3 by 3 matrix which produced the following elimination coefficients and rules: step1: row 1 is multiplied by -2 and then added to row 2; step2: row 1 is multiplied by 3 and then added to row 3; step2: row 2 is multiplied by 1 and then added to row 3. 1.1: Find the elementary matrices, E1 ; E2 ; and E3 generated by this gaussian...
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- Homework3 LU factorization Problem 1: Consider a gaussian elimination performed on a 3 by 3 matrix which produced the following elimination coefficients and rules: step1: row 1 is multiplied by -2 and then added to row 2; step2: row 1 is multiplied by 3 and then added to row 3; step2: row 2 is multiplied by 1 and then added to row 3. 1.1: Find the elementary matrices, E1 ; E2 ; and E3 generated by this gaussian elimination. 1.2: Find the matrix L associated with this procedure. Is there an easier to way find L? Problem 2 Find the inverse of the following square matrices: Note: If a matrix A is invertible then so is its transpose and AT . 1 0 A = 0 5 0
-1
= A-1
T
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0; 0 1
1 0 B = 0 0 0
0 1 0 0 0
0 0 0 0 0 0 1 -4 0 0 1 0 0 0 1
P...
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