independent equation वाक्य
उदाहरण वाक्य
मोबाइल
- An elastostatic boundary value problem for an isotropic-homogeneous media is a system of 15 independent equations and equal number of unknowns ( 3 equilibrium equations, 6 strain-displacement equations, and 6 constitutive equations ).
- There will be an infinitude of other solutions only when the system of equations has enough dependencies ( linearly dependent equations ) that the number of independent equations is at most " N " & minus; 1.
- But with " M " e " " N " the number of independent equations could be as high as " N ", in which case the trivial solution is the only one.
- The number of independent equations in a system equals the rank of the augmented matrix of the system & mdash; the system's coefficient matrix with one additional column appended, that column being the column vector of constants.
- In linear systems, indeterminacy occurs if and only if the number of independent equations ( the rank of the augmented matrix of the system ) is less than the number of unknowns and is the same as the rank of the coefficient matrix.
- Well, if it's linear equations, you'd get infinitely many solutions when the system has at least one solution and the number of variables is strictly larger than the number of linearly independent equations . talk ) 19 : 38, 2 December 2008 ( UTC)
- Where m _ { ij } is the i, j-th element of M . The sum is antisymmetric with respect to indices i, j, and since the left hand side is zero when i differs from j, this leaves n ( 2n-1 ) independent equations.
- The rank of a system of equations can never be higher than [ the number of variables ] + 1, which means that a system with any number of equations can always be reduced to a system that has a number of independent equations that is at most equal to [ the number of variables ] + 1.
- For example, in linear algebra if the number of constraints ( independent equations ) in a system of linear equations equals the number of unknowns then precisely one solution exists; if there are fewer independent equations than unknowns, an infinite number of solutions exist; and if the number of independent equations exceeds the number of unknowns, then no solutions exist.
- For example, in linear algebra if the number of constraints ( independent equations ) in a system of linear equations equals the number of unknowns then precisely one solution exists; if there are fewer independent equations than unknowns, an infinite number of solutions exist; and if the number of independent equations exceeds the number of unknowns, then no solutions exist.
- For example, in linear algebra if the number of constraints ( independent equations ) in a system of linear equations equals the number of unknowns then precisely one solution exists; if there are fewer independent equations than unknowns, an infinite number of solutions exist; and if the number of independent equations exceeds the number of unknowns, then no solutions exist.
- For if there are at least as many independent equations as unknowns that will eliminate any stretches of overlap of the equations'surfaces in the geometric space of the unknowns ( aside from possibly a single point ); and if the rank of the augmented matrix exceeds ( necessarily by one if at all ) the rank of the coefficient matrix then the equations jointly contradict each other.
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