An mxn 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.3 4 7 40 1 4 60 0 2 80 0 0 1Choose the correct answer below.O A. A square upper triangular matrix is invertible when the matrix is equal to its own transpose. For such a matrix A, A = A' means that the equation Ax = b has at least one solution for each b in R".O B. 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 nxn identity matrix.OC. 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 nxn square upper triangular matrix, has no solution for at least one b inR".O D. 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 nxn matrix has n pivot positions.

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An mxn 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.

An mxn 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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 56EQ

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Question

An mxn 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.
3 4 7 4
0 1 4 6
0 0 2 8
0 0 0 1
Choose the correct answer below.
O A. A square upper triangular matrix is invertible when the matrix is equal to its own transpose. For such a matrix A, A = A' means that the equation Ax = b has at least one solution for each b in R".
O B. 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 nxn identity matrix.
OC. 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 nxn square upper triangular matrix, has no solution for at least one b in
R".
O D. 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 nxn matrix has n pivot positions.

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