What is the determinant if there is no solution?
If the determinant of a matrix is zero, then the linear system of equations it represents has no solution. In other words, the system of equations contains at least two equations that are not linearly independent.
What happens when a linear equation has no solution?
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.
How do you determine if a linear system has no solution?
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
What does a determinant of 0 mean?
When the determinant of a matrix is zero, the volume of the region with sides given by its columns or rows is zero, which means the matrix considered as a transformation takes the basis vectors into vectors that are linearly dependent and define 0 volume.
Which is not a possible type of solution of a system of linear equations?
A system of linear equations has one solution when the graphs intersect at a point. No solution. A system of linear equations has no solution when the graphs are parallel.
How do you prove a system of equations has no solution?
When two equations have the same slope but different y-axis, they are parallel. Since there are no intersection points, the system has no solutions.
Why would an equation have no solution?
Explanation: When finding how many solutions an equation has you need to look at the constants and coefficients. The coefficients are the numbers alongside the variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.
What is an example of an equation with no solution?
The last type of equation is known as a contradiction, which is also known as a No Solution Equation. This type of equation is never true, no matter what we replace the variable with. As an example, consider 3x + 5 = 3x – 5. This equation has no solution.
Which system of equations have no solution?
inconsistent system
An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect. A dependent system has infinitely many solutions. The lines are exactly the same, so every coordinate pair on the line is a solution to both equations.
Is it possible for a homogeneous system of linear equations to have no solution?
No, homogeneous system of linear equations have either one or infinitely many solutions. The trivial solution is when all variables are assigned to be 0.
When using Cramer’s rule if D 0 then the system of linear equations is inconsistent?
When the determinant of the coefficient matrix D is zero, the formulas of Cramer’s rule are undefined. In this case, the system is either dependent or inconsistent depending on the values of Dx and Dy. When D=0 and both Dx=0 and Dy=0 the system is dependent.