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5.13 A square matrix is a matrix that has an equal number of rows and columns. In mathematics, m x m matrix is called the square matrix of order m. If we multiply or add any two square matrices, the order of the resulting matrix remains the same. If A is a square matrix, show that det A = 0 if and only if some row is a linear combination of the others.

5.13 A square matrix is a matrix that has an equal number of rows and columns. In mathematics, m x m matrix is called the square matrix of order m. If we multiply or add any two square matrices, the order of the resulting matrix remains the same. If A is a square matrix, show that det A = 0 if and only if some row is a linear combination of the others.

Linear Algebra: A Modern Introduction
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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5.13 A square matrix is a matrix that has an equal number of rows and columns. In mathematics, m x m matrix is called the square matrix of order m. If we multiply or add any two square matrices, the order of the resulting matrix remains the same. If A is a square matrix, show that det A = 0 if and only if some row is a linear combination of the others.
Transcribed Image Text:5.13 A square matrix is a matrix that has an equal number of rows and columns. In mathematics, m x m matrix is called the square matrix of order m. If we multiply or add any two square matrices, the order of the resulting matrix remains the same. If A is a square matrix, show that det A = 0 if and only if some row is a linear combination of the others.
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