The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2.
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.
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.
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.
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.
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
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.
A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?
Radial solutions are unique linear and non-linear formula equations used in math to explain the Laplacian equation. To calculate problems, scientist must determine the function based on the variable provided in the equation.
a1/a2 is not equal to b1/b2
Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.
The boundary condition is important in solving differential equations because it provides additional information that helps determine the specific solution to the equation. It helps to define the behavior of the solution at the boundaries of the domain, ensuring that the solution is unique and accurate.
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.
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.
simultaneous 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.
It is a linear equation in the two variables x and y. A single linear equation in two variables cannot be solved for a unique pair of values of x and y. The equation is that of a straight line and any point on the line satisfies the equation.
No. The equation describes a straight line and the coordinates of any one of the infinitely many points on the line is a solution.