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It is impossible for a system of two linear equations to have exactly one solution. True or False?
False, think of each linear equation as the graph of the line. Then the unique solution (one solution) would be the intersection of the two lines.
When the equation in a linear system have different slopes then the system has what kind of solution?
It is not possible to tell. The lines could intersect, in pairs, at several different points giving no solution. A much less likely outcome is that they all intersect at a single point: the unique solution to the system.
What is cramer rule?
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
What is a unique solution in linear equations?
This is the case when there is only one set of values for each of the variables that satisfies the system of linear equations. It requires the matrix of coefficients. A to be invertible. If the system of equations is y = Ax then the unique solution is x = A-1y.
What is IVP in differential equations?
Initial Value Problem. A differential equation, coupled with enough initial conditions for there to be a unique solution. Example: y'' - 6y = exp(x) ; y'(0) = y(0) = 0
