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M313Lec05

M313Lec05 - Math 313 Lecture#5 1.4 Matrix Algebra Part II...

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Math 313 Lecture #5 § 1.4: Matrix Algebra, Part II Matrix Inversion. A real number a is invertible if there is a real number b such that ba = ab = 1; when this is the case, the real number b is called the multiplicative inverse of a , and of course, b = a - 1 = 1 /a . The only non invertible real number is 0. An n × n matrix A is said to be nonsingular or invertible if there is an n × n matrix B such that AB = BA = I ; otherwise, A is said to be singular . When a square matrix A is invertible, the matrix B for which AB = BA = I is called a multiplicative inverse of A . Can there be more than one multiplicative inverse of an invertible matrix? If B and C are multiplicative inverses of a nonsingular matrix A then B = BI = B ( AC ) = ( BA ) C = IC = C. So, there is only one multiplicative inverse of an invertible matrix; the unique multiplica- tive inverse of an invertible matrix A is denoted by A - 1 . Examples.
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M313Lec05 - Math 313 Lecture#5 1.4 Matrix Algebra Part II...

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