A square matrix is called upper triangular if all of the entries below the main diagonal are zero. Thus, the form of an upper triangular matrix is
where the entries marked * are arbitrary. A more formal definition of such a matrix
Prove that the product of two upper triangular
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Linear Algebra: A Modern Introduction
- Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why not. For simplicity, assume a 22 matrix.arrow_forwardShow that the matrix below does not have an LU factorization. A=0110arrow_forwardIn general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that .arrow_forward
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