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(i) For any three matrices of the same order, prove that (A+B)-(B+C)+(C+A)=2A. (ii)…
MATHEMATICS · Subjective · CBSE · Mathematics · Matrices · Matrices
Problem
(i) For any three matrices
A
,
B
,
C
A,\,B,\,C
A
,
B
,
C
of the same order, prove that
(
A
+
B
)
−
(
B
+
C
)
+
(
C
+
A
)
=
2
A
.
(A+B)-(B+C)+(C+A)=2A.
(
A
+
B
)
−
(
B
+
C
)
+
(
C
+
A
)
=
2
A
.
(ii) Verify the result in part (i) for the matrices
A
=
[
1
−
2
3
0
4
−
1
]
,
B
=
[
−
3
5
2
7
−
6
0
]
,
C
=
[
4
−
1
−
5
−
2
3
6
]
.
A=\begin{bmatrix}1&-2&3\\0&4&-1\end{bmatrix}, \; B=\begin{bmatrix}-3&5&2\\7&-6&0\end{bmatrix}, \; C=\begin{bmatrix}4&-1&-5\\-2&3&6\end{bmatrix}.
A
=
[
1
0
−
2
4
3
−
1
]
,
B
=
[
−
3
7
5
−
6
2
0
]
,
C
=
[
4
−
2
−
1
3
−
5
6
]
.
Show all steps explicitly.
Related theory
Matrix Operations
Matrices
Addition of matrices
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