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When its matrix is non-singular.
false
yes it can . the system may have infinitely many solutions.
Without a second independent equation, it's not a 'system' yet.
Without a second independent equation, it's not a 'system' yet.
When its matrix is non-singular.
That doesn't apply to "an" equation, but to a set of equations (2 or more). Two equations are:* Inconsistent, if they have no common solution (a set of values, for the variables, that satisfies ALL the equations in the set). * Consistent, if they do. * Dependent, if one equation can be derived from the others. In this case, this equation doesn't provide any extra information. As a simple example, one equation is the same as another equation, multiplying both sides by a constant. * Independent, if this is not the case.
consistent dependent
false
linus
A consistent system.
There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.
yes it can . the system may have infinitely many solutions.
Without a second independent equation, it's not a 'system' yet.
Without a second independent equation, it's not a 'system' yet.
An independent system of linear equations is a set of vectors in Rm, where any other vector in Rm can be written as a linear combination of all of the vectors in the set. The vector equation and the matrix equation can only have the trivial solution (x=0).
Furnace oil is the source of fuel used by the heating system to create a consistent warmth when required.