View source: R/gaussian-elimination.R
echelon | R Documentation |
Returns the (reduced) row-echelon form of the matrix A
, using gaussianElimination
.
echelon(A, B, reduced = TRUE, ...)
A |
coefficient matrix |
B |
right-hand side vector or matrix. If |
reduced |
logical; should reduced row echelon form be returned? If |
... |
other arguments passed to |
When the matrix A
is square and non-singular, the reduced row-echelon result will be the
identity matrix, while the row-echelon from will be an upper triangle matrix.
Otherwise, the result will have some all-zero rows, and the rank of the matrix
is the number of not all-zero rows.
the reduced echelon form of X
.
John Fox
A <- matrix(c(2, 1, -1, -3, -1, 2, -2, 1, 2), 3, 3, byrow=TRUE) b <- c(8, -11, -3) echelon(A, b, verbose=TRUE, fractions=TRUE) # reduced row-echelon form echelon(A, b, reduced=FALSE, verbose=TRUE, fractions=TRUE) # row-echelon form A <- matrix(c(1,2,3,4,5,6,7,8,10), 3, 3) # a nonsingular matrix A echelon(A, reduced=FALSE) # the row-echelon form of A echelon(A) # the reduced row-echelon form of A b <- 1:3 echelon(A, b) # solving the matrix equation Ax = b echelon(A, diag(3)) # inverting A B <- matrix(1:9, 3, 3) # a singular matrix B echelon(B) echelon(B, reduced=FALSE) echelon(B, b) echelon(B, diag(3))
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