18.06 -PS4 - Solved

Exercises on factorization into A = LU 

Problem 4.1: What matrix E puts A into triangular form EA = U? Multiply by E−1 = L to factor A into LU. 

 

A   

Problem 4.2: (2.6 #13. Introduction to Linear Algebra: Strang) Compute L 

and U for the symmetric matrix 
 
 
 
 

⎡ a

A = ⎢⎢  aa

⎣

a
a b b b
a b c c
a  ⎤ b  ⎥

c  ⎥⎦ . d 
Find four conditions on a, b, c, d to get A = LU with four pivots.