Chadlee88 said:i need to be able to prove that an nxn matrix with two identical columns cannot be invertible. I know that if the columns of the matrix are linearly independent then the matrix is invertible. Could some please give me a hint on how to do this proof because i really don't know where to start.
Yeh, I went back and edited my post just before I saw this.Office_Shredder said:
A matrix inverse is a mathematical concept that refers to the process of finding a matrix that, when multiplied by another matrix, results in the identity matrix. In simpler terms, it is the matrix version of division, where instead of dividing by a number, we multiply by its inverse.
Invertible matrices are important in proofs because they provide a way to solve systems of equations, and also have several useful properties that make them useful in various mathematical operations. In addition, the invertibility of a matrix is often a key factor in determining the existence of solutions to certain problems.
A matrix is invertible if its determinant is non-zero. This means that the matrix has an inverse that can be found using various methods, such as Gaussian elimination or the adjugate formula. In addition, square matrices with full rank are always invertible.
No, a matrix cannot be invertible if it has a row or column of zeros. This is because a row or column of zeros will result in a determinant of zero, making the matrix non-invertible. However, if a matrix has a zero entry in a non-diagonal position, it can still be invertible.
Yes, all invertible matrices are square matrices. This is because a non-square matrix cannot have an inverse, as the inverse must have the same number of rows and columns as the original matrix in order for the multiplication to result in the identity matrix.