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3-46
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)a1(A-E)1(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)
a1(A-E)1(A)!a(CATALOG)
a6(SYBL)4(9)c~c(–1)ww
• 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
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