A nonsingular matrix is a square matrix that has a determinant that is not equal to 0. This means that the matrix has an inverse and can be solved for a unique solution.
It is important to show that a nonsingular matrix has a unique solution because it guarantees that the system of equations represented by the matrix has only one solution. This is useful in many applications, including linear programming, optimization, and engineering problems.
To prove that a nonsingular matrix has a unique solution, we can use the determinant of the matrix. If the determinant is not equal to 0, then the matrix is nonsingular and has an inverse. This inverse can then be used to solve for a unique solution.
If a matrix is singular, it means that the determinant is equal to 0 and the matrix does not have an inverse. This can lead to multiple solutions or no solutions at all for the system of equations represented by the matrix.
No, a nonsingular matrix can only have one solution. This is because the inverse of a nonsingular matrix is unique, and the inverse is used to find the solution to a system of equations represented by the matrix.