A matrix proof is a mathematical method used to show the validity or truth of a statement involving matrices. It involves using mathematical operations and properties to manipulate matrices and arrive at a conclusion.
A matrix is considered singular if its determinant is equal to zero. This means that the matrix is not invertible and does not have a unique solution.
To prove that C is singular, we can use the fact that Ax=Bx to substitute for A and B in the equation C=A-B. This will give us the equation C=0, which means that the determinant of C is equal to zero. Therefore, C is singular.
If x is equal to zero, then the equation Ax=Bx becomes 0=0, which does not provide any useful information. By assuming that x is nonzero, we can manipulate the equations to prove that C is singular.
Yes, this proof can be extended to matrices of any size. As long as the equations Ax=Bx and C=A-B hold true, then it can be proven that C is singular.