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2331_Notes_5o3_fill - Math 2331 Linear Algebra Section 5.3...

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Math 2331 Linear Algebra Section 5.3 Cramer's Rule, Inverses and Volumes Cramer's Rule This is a way to solve Ax = b using determinants If det(A) is not zero (i.e. A is square and invertible), 1. Ax = b is solvable for any b 2. Cramer's rule can solve for each component of x individually To find the jth component of b, first replace the jth column of A with the vector b and let's call this matrix j B Then det( ) det( ) j j B x A = Example: Use Cramer's Rule to find the solution to 1 2 1 2 3 2 6 5 4 x x x x = + = 8
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