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 does it mean for determinant to be zero?

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.

What does it mean when a system of equations has 0 0?

2 Answers. If you end with 0=0 , then it means that the left-hand side and the right-hand side of the equation are equal to each other regardless of the values of the variables involved; therefore, its solution set is all real numbers for each variable.

What does it mean when a system of equations has no solution?

inconsistent
Systems of equations can be classified by the number of solutions. 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 is a non zero solution?

Answer: A solution or example that is not trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5y = 0 has the trivial solution (0, 0).

What happens when the determinant of a matrix is 0?

Ans: If the determinant of a matrix is zero,then the matrix is called as a singular matrix. Inverse of such kind of matrix can’t be found out as Inverse of a matrix=Adjoint of the matrix/Determinant of the matrix. If the determinant is equal to zero then that matrix is not invertible .

Can determinant be zero value?

If two rows of a matrix are equal, its determinant is zero.

Why is a matrix not invertible if determinant is 0?

[Non-square matrices do not have determinants.] The determinant of a square matrix A detects whether A is invertible: If det(A) is not zero then A is invertible (equivalently, the rows of A are linearly independent; equivalently, the columns of A are linearly independent).

What does 0 0 mean on a graph?

the origin
The point given by (0,0) is called the origin. If a graph passes through the origin then the x-intercept and the y-intercept are at the same point and are therefore equal. This is the only point where the x- and y- coordinates are equal.

When there is no solution of a system of equations then the system is called system of equations?

A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel. A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.

What is a zero solution?

The solution x = 0 means that the value 0 satisfies. the equation, so there is a solution. ” No solution” means that there is no value, not even 0, which would satisfy the equation.