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Exam 3: Matrices

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Question 41

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Find an LU factorization of

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Question 42

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

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Question 43

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

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

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

Use the quick formula to determine the inverse of

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

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

Determine if the matrix is a stochastic matrix.

Evaluate 3AB, where

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

If is a square invertible matrix, and then

Evaluate AB, where

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

Find an LU factorization of

Determine if the given matrix is regular.