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MATH 330 H44

# MATH 330 H44 - Math 330 Homework 4.4(Pages 254,255(8 Find...

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Unformatted text preview: Math 330 Homework 4.4 (Pages 254,255) (8) Find the coordinate vector [ vectorx ] B relative to the basis B = { vector b 1 , vector b 2 , vector b 3 } where vector b 1 = 1 3 , vector b 2 = 2 1 8 , vector b 1 = 1- 1 2 , vectorx = 3- 5 4 SOLUTION: We must find weights α 1 , α 2 , α 3 so that α 1 vector b 1 + α 2 vector b 2 + α 3 vector b 3 = vectorx . This is equivalent to the following augmented matrix system Avectorα = vectorx where vectorα = α 1 α 2 α 3 . 1 2 1 3 0 1- 1- 5 3 8 2 4 R 3 ← R 3- 3 R 1 = ⇒ 1 2 1 3 0 1- 1- 5 0 2- 1- 5 R 3 ← R 3- 2 R 2 = ⇒ 1 2 1 3 0 1- 1- 5 0 0 1 5 R 1 ← R 1- 2 R 2 ⇒ 1 0 3 13 0 1- 1- 5 0 0 1 5 ( R 1 ,R 2) ← ( R 1- 3 R 3 ,R 2+ R 3) = ⇒ 1 0 0- 2 0 1 0 0 0 1 5 ⇒ [ vectorx ] B = - 2 5 (10) Find the change-of-coordinates matrix from...
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MATH 330 H44 - Math 330 Homework 4.4(Pages 254,255(8 Find...

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