lecture11hout

lecture11hout - MATH 006 Calculus and Linear Algebra...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 11) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 12 Outline 1 Matrix Equations 2 An Application Albert Ku (HKUST) MATH 006 2 / 12 Matrix Equations Matrix Equations Consider the following system x 1- x 2 + x 3 = 1 2 x 2- x 3 = 1 2 x 1 + 3 x 2 = 1 We can rewrite the system as a matrix equation . The idea is to define the following matrices: A = 1- 1 1 2- 1 2 3 , x = x 1 x 2 x 3 , b = 1 1 1 Albert Ku (HKUST) MATH 006 3 / 12 Matrix Equations Then we observe that the system can be rewritten as Ax = b . This is a matrix equation whose unknown is x . To solve a general matrix equation of the form Ax = b , we first assume that A is an invertible square matrix (a square matrix whose inverse exists). Then we have A- 1 Ax = A- 1 b ⇒ Ix = A- 1 b ⇒ x = A- 1 b That is to say, if we can find A- 1 , then we can solve the matrix equation and hence the system....
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This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture11hout - MATH 006 Calculus and Linear Algebra...

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