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u Reduced 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:
Matrix A =
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:
Matrix A =
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 b
c d
A
–1
=
1
ad – bc
d–b
–c a
Note that ad – bc ≠ 0.
2 −1 3 19
1 1 −5 −21
0 4 3 0
2 −1 3 19
1 1 −5 −21
0 4 3 0
1 2
3 4
1 2
3 4