Let A , B , and C be m × n matrices such that A + C = B + C . The following statements are steps in a proof that A = B . Using Theorem 7, provide justification for each of the assertions. a) There exists an m × n matrix O such that A = A + O . b) There exists an m × n matrix D such that A = A + C + D . c) A = A + C + D = B + C + D . d) A = B + C + D . e) A = B + O . f) A = B
Let A , B , and C be m × n matrices such that A + C = B + C . The following statements are steps in a proof that A = B . Using Theorem 7, provide justification for each of the assertions. a) There exists an m × n matrix O such that A = A + O . b) There exists an m × n matrix D such that A = A + C + D . c) A = A + C + D = B + C + D . d) A = B + C + D . e) A = B + O . f) A = B
Solution Summary: The author explains that the assertion A+O=A is justified by the property 3 of theorem 7.
Let
A
,
B
,
and
C
be
m
×
n
matrices such that
A
+
C
=
B
+
C
. The following statements are steps in a proof that
A
=
B
. Using Theorem 7, provide justification for each of the assertions.
a) There exists an
m
×
n
matrix
O
such that
A
=
A
+
O
.
b) There exists an
m
×
n
matrix
D
such that
A
=
A
+
C
+
D
.
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