Casio FX-CG10 Software User Guide - Page 101
Reduced Row Echelon Form, Matrix Inversion, OPTN], Rref], Example
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u Reduced Row Echelon Form This command finds the reduced row echelon form of a matrix. [OPTN]-[MAT]-[Rref] Example To find the reduced row echelon form of the following matrix: Matrix A = 2 −1 3 19 1 1 −5 −21 043 0 K2(MAT)6(g)5(Rref) 6(g)1(Mat)av(A)w • The row echelon form and reduced row echelon form operation may not produce accurate results due to dropped digits. u Matrix Inversion [x-1] Example To invert the following matrix: 1 2 Matrix A = 3 4 K2(MAT)1(Mat) av(A)!)(x-1)w • Only square matrices (same number of rows and columns) can be inverted. Trying to invert a matrix that is not square produces an error. • A matrix with a determinant of zero cannot be inverted. Trying to invert a matrix with determinant of zero produces an error. • Calculation precision is affected for matrices whose determinant is near zero. • A matrix being inverted must satisfy the conditions shown below. A A-1 = A-1 A = E = 1 0 0 1 The following shows the formula used to invert Matrix A into inverse matrix A-1. A = A-1= a b c d 1 ad - bc d -b -c a Note that ad - bc ≠ 0. 2-55