[SOLVED] MA232 Homework 2

Problem 1 [20pts] Which matrices E21,E31 produce zero in the (2,1) re- spectively (3, 1) position of E21 · A respectively E31 · A for

210 A=-2 0 1

853
Find the single matrix E that produces both zeros at once and calculate E·A.

Problem 2 [20pts] Use the Gauss elimination method in order to find the inverses of the following matrices:

0002 3200 A=0030, B=4300

 0400 0065

5000 0076

 2 -1 0  Problem 3 [20pts] Factor the symmetric matrix A =  -1 2 -1  as

0 -1 2

A = LDLT .

b1 
Problem 4 [20pts] For which vectors b = b2 the following system of

b3
1 1 1x1 b1

equationshasasolutionA= 0 0 1 x2=b2? 001×3 b3

Problem 5 [20 pts] Reduce the following matrices to their row reduced 12246 242

echelonform:A=1 2 3 6 9, B=0 4 4 00123 088

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