3.1 Solving linear equations Introduction
... the same as the right-hand side. So, x = 4 is a solution. We say that x = 4 satisfies the equation. (b) Substituting x = 2 into the left-hand side we find 3(2) − 2 which equals 4. Clearly the left-hand side is not equal to 10 and so x = 2 is not a solution. The number x = 2 does not satisfy the equa ...
... the same as the right-hand side. So, x = 4 is a solution. We say that x = 4 satisfies the equation. (b) Substituting x = 2 into the left-hand side we find 3(2) − 2 which equals 4. Clearly the left-hand side is not equal to 10 and so x = 2 is not a solution. The number x = 2 does not satisfy the equa ...
The quadprog Package
... matrix of integers. The first element of each column gives the number of nonzero elements in the corresponding column of the matrix A. The following entries in each column contain the indexes of the rows in which these non-zero elements are. ...
... matrix of integers. The first element of each column gives the number of nonzero elements in the corresponding column of the matrix A. The following entries in each column contain the indexes of the rows in which these non-zero elements are. ...
Matrices and RRE Form Notation. R is the real numbers, C is the
... and B is obtained from A by a sequence of elementary row operations. Then the solutions to the system of linear equations corresponding to A and the system of linear equations corresponding to B are the same. To prove this theorem, it suffices (by induction) to verify it when B is obtained from A by ...
... and B is obtained from A by a sequence of elementary row operations. Then the solutions to the system of linear equations corresponding to A and the system of linear equations corresponding to B are the same. To prove this theorem, it suffices (by induction) to verify it when B is obtained from A by ...