{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

solset2

# solset2 - Problem Set#2 Solutions 2.4#33 If the three...

This preview shows pages 1–2. Sign up to view the full content.

Problem Set #2 Solutions § 2.4 #33: If the three solutions in Question 32 are ~ x 1 = (1 , 1 , 1) and ~ x 2 = (0 , 1 , 1) and ~ x 3 = (0 , 0 , 1) , solve A~x = ~ b when ~ b = (3 , 5 , 8) . Challenge problem: What is A ? Solution: Needed: A ~ x 1 = 1 0 0 , A ~ x 2 = 0 1 0 , A ~ x 3 = 0 0 1 If we let ~ x 1 = 1 1 1 , ~ x 2 = 0 1 1 , ~ x 3 = 0 0 1 And since we know A~x = b , we know the following: A~x = 3 5 8 = 3 1 0 0 + 5 0 1 0 + 8 0 0 1 = 3( A ~ x 1 ) + 5( A ~ x 2 ) + 8( A ~ x 3 ) = A (3 ~ x 1 ) + A (5 ~ x 2 ) + A (8 ~ x 3 ) ~x = 3 ~ x 1 + 5 ~ x 2 + 8 ~ x 3 . Recommended: A ~ x 3 = A 0 0 1 = Last column of A = 0 0 1 A = a 11 a 12 0 a 21 a 22 0 a 31 a 32 1 ~ x 2 = 0 1 1 : A ~ x 2 = A 0 1 0 + 0 0 1 = A 0 1 0 + 0 0 1 = 0 1 0 A 0 0 1 = a 12 a 22 a 23 = 0 1 - 1 A = a 11 0 0 a 21 1 0 a 31 - 1 1 Continued...

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}