Casio fx-CG20 uMatrix Inversion, uReduced Row Echelon Form, −21, [x–1], Example, Example, Matrix A, Matrix A, To invert the following matrix:

uReduced Row Echelon Form							[OPTN]-[MAT]-[Rref]
This command finds the reduced row echelon form of a matrix.
Example	To find the reduced row echelon form of the following matrix:
			2	−1	3	19
	Matrix A =	1		1	−5	−21
			0	4	3	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.

uMatrix Inversion				[x–1]
Example	To invert the following matrix:
	Matrix A =	1	2
			4
		3

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–1A = E =	1	0
	0	1

The following shows the formula used to invert Matrix A into inverse matrix A–1.

A =			a	b
			c	d
A	–1	=		1	d –b
			ad – bc		–c a

Note that ad – bc ≠ 0.

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