Math 54 - Midterm 01 Review, Spring 2006 (2)

Math 54 - Midterm 01 Review, Spring 2006 (2) - MATH 54...

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MATH 54 Midterm 1 Review Edward Carter February 13, 2006 1 Linear Equations and Matri- ces 1.1 Things to Know How to row-reduce a matrix, and how to read the solution set of a linear system from its row- reduced matrix. If A is m × n and B is n × q , then C = AB is m × q , and C ij = n k =1 A ik B kj . In general AB 6 = BA . However, A ( BC ) = ( AB ) C , and A ( B + C ) = AB + AC . If A is a square matrix, then the inverse A - 1 is a matrix such that A - 1 A = AA - 1 = I , if such a matrix exists. In this case, A is called invertible. The inverse of a matrix A is unique if it exists. If A and B are both invertible, so is AB , and ( AB ) - 1 = B - 1 A - 1 . How to compute inverses via row-reduction. The three types of elementary matrices. Let A be an n × n matrix. Then the following are equivalent: A is invertible. AX = B has a unique solution for any B . AX
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This note was uploaded on 02/20/2010 for the course AS a taught by Professor 11 during the Spring '10 term at École Normale Supérieure.

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Math 54 - Midterm 01 Review, Spring 2006 (2) - MATH 54...

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