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Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence
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Label the following statements as true or false. (a) An elementary matrix is always

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QUESTION:

Label the following statements as true or false. (a) An elementary matrix is always square. The only entries of an elementary matrix are zeros and ones. The n x n identity matrix is an elementary matrix. The product of two n x n elementary matrices is an elementary matrix. The inverse of an elementary matrix is an elementary matrix. The sum of two nxn elementary matrices is an elementary matrix. The transpose of an elementary matrix is an elementary matrix. If B is a matrix that can be obtained by performing an elementary row operation on a matrix A, then B can also be obtained by performing an elementary column operation on A. If B is a matrix that can be obtained by performing an elementary row operation on a matrix A, then A can be obtained by performing an elementary row operation on B.

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QUESTION:

Label the following statements as true or false. (a) An elementary matrix is always square. The only entries of an elementary matrix are zeros and ones. The n x n identity matrix is an elementary matrix. The product of two n x n elementary matrices is an elementary matrix. The inverse of an elementary matrix is an elementary matrix. The sum of two nxn elementary matrices is an elementary matrix. The transpose of an elementary matrix is an elementary matrix. If B is a matrix that can be obtained by performing an elementary row operation on a matrix A, then B can also be obtained by performing an elementary column operation on A. If B is a matrix that can be obtained by performing an elementary row operation on a matrix A, then A can be obtained by performing an elementary row operation on B.

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Few statements are given and the objective is to state whether those are true or false.

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