Algorithm for Matrix Inversion: A Comprehensive Guide
Explore the step-by-step algorithm for finding the inverse of a matrix. Learn how to determine if a matrix is invertible, transform it into its Reduced Row Echelon Form (RREF), and find the inverse matrix. Follow along with detailed explanations and visual aids to master the concept of matrix inversion.
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Presentation Transcript
Find Inverse Find Inverse of of Matrix Matrix
2 X 2 Matrix ? ? ? ? =? ? ? ? 1= Find ?,?,?, ? ? ? ? =1 0 1 ? ? ? ? 0 1 ? ? ? ? 1= ? ?? ?? If ?? ?? = 0, A is not invertible.
Algorithm for Matrix Inversion Let A be an n x n matrix. A is invertible if and only if the reduced row echelon form of A is In ?? ?2?1? = ? ? 1 = ?? ? 1= ?? ?2?1
Algorithm for Matrix Inversion Let A be an n x n matrix. Transform [ A In] into its RREF [ R B ] R is the RREF of A B is a nxn matrix (not RREF) If R = In, then A is invertible B = A-1 ?? ?2?1? = ? ?? ?? ?2?1 ? 1 ??
Algorithm for Matrix Inversion In Invertible RREF
Algorithm for Matrix Inversion Let A be an n x n matrix. Transform [ A In] into its RREF [ R B ] R is the RREF of A B is a nxn matrix (not RREF) If R = In, then A is invertible B = A-1 To find A-1C, transform [ A C ] into its RREF [ R C ] C = A-1C ? 1? = ? ?? ?2?1? ? 1 ?? ?2?1? ? ??
