True or False? In Exercises 41 and 42 , determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) The identity matrix is an elementary matrix. (b) If E is an elementary matrix, then 2 E is an elementary matrix. (c) The inverse of an elementary matrix is an elementary matrix.
True or False? In Exercises 41 and 42 , determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) The identity matrix is an elementary matrix. (b) If E is an elementary matrix, then 2 E is an elementary matrix. (c) The inverse of an elementary matrix is an elementary matrix.
Solution Summary: The author explains that the identity matrix is an elementary matrix. It must satisfy the following condition to determine whether it is true or not.
True or False? In Exercises
41
and
42
, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) The identity matrix is an elementary matrix.
(b) If
E
is an elementary matrix, then
2
E
is an elementary matrix.
(c) The inverse of an elementary matrix is an elementary matrix.
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