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Question
If A=⎡⎢⎣12−35021−11⎤⎥⎦,B=⎡⎢⎣3−12425203⎤⎥⎦ and C=⎡⎢⎣4120321−23⎤⎥⎦, then compute (A+B) and (B−C). Also, verify that A+(B−C)=(A+B)−C.
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Solution
Calculating (A+B) and (B−C)
Given : A=⎡⎢⎣12−35021−11⎤⎥⎦,B=⎡⎢⎣3−12425203⎤⎥⎦ and C=⎡⎢⎣4120321−23⎤⎥⎦
Now, A+B=⎡⎢⎣12−35021−11⎤⎥⎦+⎡⎢⎣3−12425203⎤⎥⎦
=⎡⎢⎣1+32−1−3+25+40+22+51+2−1+01+3⎤⎥⎦
=⎡⎢⎣41−19273−14⎤⎥⎦
And B−C=⎡⎢⎣3−12425203⎤⎥⎦−⎡⎢⎣4120321−23⎤⎥⎦
=⎡⎢⎣3−4−1−12−24−02−35−22−10−(−2)3−3⎤⎥⎦
=⎡⎢⎣−1−204−13120⎤⎥⎦
Solve for proving
A+(B−C)=(A+B)−C
Taking L.H.S.
L.H.S.=A+(B−C)
=⎡⎢⎣12−35021−11⎤⎥⎦+⎡⎢⎣−1−204−13120⎤⎥⎦
=⎡⎢⎣1−12−2−3+05+40−12+31+1−1+21+0⎤⎥⎦
=⎡⎢⎣00−39−15211⎤⎥⎦
R.H.S.=(A+B)−C
=⎡⎢⎣41−19273−14⎤⎥⎦−⎡⎢⎣4120321−23⎤⎥⎦
=⎡⎢⎣4−41−1−1−29−02−37−23−1−1+24−3⎤⎥⎦
=⎡⎢⎣00−39−15211⎤⎥⎦
So, L.H.S.=R.H.S.
Hence it is proved that
A+(B−C)=(A+B)−C
Given : A=⎡⎢⎣12−35021−11⎤⎥⎦,B=⎡⎢⎣3−12425203⎤⎥⎦ and C=⎡⎢⎣4120321−23⎤⎥⎦
Now, A+B=⎡⎢⎣12−35021−11⎤⎥⎦+⎡⎢⎣3−12425203⎤⎥⎦
=⎡⎢⎣1+32−1−3+25+40+22+51+2−1+01+3⎤⎥⎦
=⎡⎢⎣41−19273−14⎤⎥⎦
And B−C=⎡⎢⎣3−12425203⎤⎥⎦−⎡⎢⎣4120321−23⎤⎥⎦
=⎡⎢⎣3−4−1−12−24−02−35−22−10−(−2)3−3⎤⎥⎦
=⎡⎢⎣−1−204−13120⎤⎥⎦
Solve for proving
A+(B−C)=(A+B)−C
Taking L.H.S.
L.H.S.=A+(B−C)
=⎡⎢⎣12−35021−11⎤⎥⎦+⎡⎢⎣−1−204−13120⎤⎥⎦
=⎡⎢⎣1−12−2−3+05+40−12+31+1−1+21+0⎤⎥⎦
=⎡⎢⎣00−39−15211⎤⎥⎦
R.H.S.=(A+B)−C
=⎡⎢⎣41−19273−14⎤⎥⎦−⎡⎢⎣4120321−23⎤⎥⎦
=⎡⎢⎣4−41−1−1−29−02−37−23−1−1+24−3⎤⎥⎦
=⎡⎢⎣00−39−15211⎤⎥⎦
So, L.H.S.=R.H.S.
Hence it is proved that
A+(B−C)=(A+B)−C
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