1.3.4 Gauss-Jordan Method
Chapter 1: Chapter 1 · MATHEMATICS-VOLUME 1 · EN medium
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Let A be a non-singular square matrix of order n . Let B be the inverse of A . Then, we have AB BA I n . By the property of I n , we have A I A AI Consider the equation A = I A …( ) Since A is non-singular, pre-multiplying by a sequence of elementary matrices (row operations) on both sides of ( ), A on the left-hand-side of ( ) is transformed to the identity matrix I n and the same sequence of elementary matrices (row operations) transforms I n of the right-hand-side of ( ) to a matrix B . So, equation ( ) transforms to I
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 33
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Let A be a non-singular square matrix of order n . Let B be the inverse of A . Then, we have AB BA I n . By the property of I n , we have A I A AI Consider the equation A = I A …( ) Since A is non-singular, pre-multiplying by a sequence of elementary matrices (row operations) on both sides of ( ), A on the left-hand-side of ( ) is transformed to the identity matrix I n and the same sequence of elementary matrices (row operations) transforms I n of the right-hand-side of ( ) to a matrix B .
So, equation ( ) transforms to I
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