LINEAR ALGEBRA: EXAM 3 TRUE OR
FALSE QUESTIONS WITH CORRECT
ANSWERS
An elementary matrix is always square. - Answer-True
The only entries of an elementary matrix are zeros and ones. - Answer-False
The nxn identity matrix is an elementary matrix. - Answer-True
The product of two nxn elementary matrices is an elementary matrix. - Answer-False
The inverse of an elementary matrix as an elementary matrix - Answer-True
The sum of two nxn elementary matrices is an elementary matrix - Answer-False
The transpose of an elementary matrix is an elementary matrix. - Answer-True
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. - Answer-False
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. -
Answer-True
The rank of a matrix is equal to the number of its nonzero columns. - Answer-False
The product of two matrices always has rank equal to the lesser of the ranks of the two
matrices. - Answer-False
The mxn zero matrix is the only x n matrix having rank 0. - Answer-True
Elementary row operations preserve rank. - Answer-True
Elementary column operations do not necessarily preserve rank. - Answer-False
The rank of a matrix is equal to the maximum number of linearly independent rows in
the matrix. - Answer-True
The inverse of a matrix can be computed exclusively by means of elementary row
operations. - Answer-True
FALSE QUESTIONS WITH CORRECT
ANSWERS
An elementary matrix is always square. - Answer-True
The only entries of an elementary matrix are zeros and ones. - Answer-False
The nxn identity matrix is an elementary matrix. - Answer-True
The product of two nxn elementary matrices is an elementary matrix. - Answer-False
The inverse of an elementary matrix as an elementary matrix - Answer-True
The sum of two nxn elementary matrices is an elementary matrix - Answer-False
The transpose of an elementary matrix is an elementary matrix. - Answer-True
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. - Answer-False
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. -
Answer-True
The rank of a matrix is equal to the number of its nonzero columns. - Answer-False
The product of two matrices always has rank equal to the lesser of the ranks of the two
matrices. - Answer-False
The mxn zero matrix is the only x n matrix having rank 0. - Answer-True
Elementary row operations preserve rank. - Answer-True
Elementary column operations do not necessarily preserve rank. - Answer-False
The rank of a matrix is equal to the maximum number of linearly independent rows in
the matrix. - Answer-True
The inverse of a matrix can be computed exclusively by means of elementary row
operations. - Answer-True
