An m X n upper triangular matrix is one whose entries below the main diagonal ar

Question

An m X n upper triangular matrix is one whose entries below the main diagonal are zeros, as is shown in the matrix to the right. When is a square upper triangular matrix invertible? Justify your answer. Choose the correct answer below. A. A square upper triangular matrix is invertible when the matrix is equal to its own transpose. For such a matrix A, A = T means that the equation Ax = b has at least one solution for each b in R. B. A square upper triangular matrix is invertible when all entries on the main diagonal are ones. If any entry on the main diagonal is not one, then the equation Ax = b, where A is an n X n square upper triangular matrix, has no [3 4 7 4 0 1 4 6 0 0 2 8 0 0 0 1] solution for at least one b in R . C. A square upper triangular matrix is invertible when all entries on its main diagonal are nonzero. If all of the entries on its main diagonal are nonzero, then the n x n matrix has n pivot positions. D. A square upper triangular matrix is invertible when all entries above the main diagonal are zeros as well. This means that the matrix is row equivalent to the n X n identity matrix.

Explanation / Answer

Answer : C

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