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Lecture+23--Inverse+matrix+_+Condition+number

# Lecture+23--Inverse+matrix+_+Condition+number - Chapter 10...

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Chapter 10 Matrix Inverse and Condition

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How do we get inverse [ A ] 1 ? Consider solving [ A ]{ xi } = { bi } with Put together x’s to get inverse of [A] as {x1,x2,x3,x4} Matrix Inverse Sequentially! { } { } { } { } 1 2 3 4 1 0 0 0 0 1 0 0 , , , 0 0 1 0 0 0 0 1 b b b b                         = = = =                                
Matrix Inverse Inverse matrix can be obtained using Gaussian-Jordan method * Consider: A= A-1 =? * Add unit vectors to * Pivoting : Row 2 Row 1 I - 2 0 1 1 0 3 2 1 1 1 0 0 0 1 0 0 0 1 1 1 2 3 0 1 1 0 2 - 3 0 1 1 1 2 1 0 2 0 1 0 1 0 0 0 0 1 -

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Matrix Inverse * Gaussian elimination Reduce the upper triangular matrix to to obtain identity matrix I on the left of the augmented matrix U Row 3 / 1.6667 Row 2 - (Row 3 )*1.6667 Row 1 - (Row 3)* 1 1 2 3 1 2 3 0 1 3 0 0 1 1 0 1 0 1.66 .333 67 0 0 1.66 3 0 0 0.33 67 33 1 - - -
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