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Unformatted text preview: Jessica Chung & Derek Hui Week 10 QMA PASS | 2006 S2 | Tues, 3-4pm | QUAD G042 Questions? Email us: [email protected] , [email protected] 1/2 SOLVING LINEAR EQUATIONS USING MATRICES Matrix multiplication is used to simplify the solving of linear equations. You’ve just learnt the adjoint method – we will not show you how to solve linear equations by applying this method! Recall the steps in finding the inverse of a matrix using the adjoint method: 1. Find the determinant of A If |A| = 0, the inverse does not exist 2. Find the matrix of minors 3. Convert the minors to cofactors by multiply by (-1) i+j 4. Transpose the matrix to get the adjoint 5. Inverse is given by: 1 1 Adjoint A A A- = × In matrix notation, a system of equations can be written as: Ax = b . Thus, having found the inverse of A, or A-1 , we solve for x according to: x = A-1 b . >> DON’T FORGET: ORDER OF MULTIPLICATION WHEN WORKING WITH MATRICES IS IMPORTANT! << Hence, having completed the 5 steps above, we solve a set of linear equations with a 6 th step as follows:...
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- Three '08
- Linear Algebra, Invertible matrix, 2 WEEK, Transpose, Jessica Chung