Exam 3: Matrices

Determine if the given linear transformation is invertible, and if so, find .

If is any square matrix, then the matrix is symmetric.

Use an augmented matrix and row operations to find the inverse of

Use the quick formula to determine the inverse of

Determine if the matrix is a stochastic matrix.

Evaluate AB, where

Use an augmented matrix and row operations to find the inverse of

Determine if the given matrix is regular.

Find an LU factorization of

If is a square invertible matrix, and then

Evaluate 3AB, where

Determine if the given linear transformation is invertible, and if so, find .

Use an augmented matrix and row operations to find the inverse of

Find an LU factorization of

If both A and B are matrices such that their product AB has an LU factorization, then both A and B have LU factorizations.

If and are stochastic matrices, then is a stochastic matrix.