Reduced Row Echelon Form; Matrix Inversion - Casio FX-CG20 AU User Manual

u Reduced Row Echelon Form
This command finds the reduced row echelon form of a matrix.
Example To find the reduced row echelon form of the following matrix:
Matrix A =
K2(MAT/VCT) 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
Example To invert the following matrix:
Matrix A =
K2(MAT/VCT) 1(Mat)
av(A) !)(
• 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.
–1 –1
A A = A A = E =
The following shows the formula used to invert Matrix A into inverse matrix A
a b
A =
c d
1
–1
A =
ad – bc
Note that ad – bc ≠ 0.
2 2 −1 −1 3 3
1 1 1 1 −5 −5
0 0 4 4 3 3
1 1 2 2
3 3 4 4
) w
x
–1
1 0
0 1
d –b
–c a
2-56
19 19
−21 −21
0 0
[OPTN] - [MAT/VCT] - [Rref]
–1 .
x –1
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