Given A = 1 2 −2 3 , B = −2 −1 1 2 and C = 0 3 2 −1 ,find A + 2B – C. They are matrix equation
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Answer:
Let A=[
a
b
c
d
]
so, [
2
3
1
2
]A[
−3
5
2
−3
]=[
1
0
0
1
]
⇒[
2
3
1
2
][
a
b
c
d
][
−3
5
2
−3
]=[
1
0
0
1
]
⇒[
2a+b
3a+2b
2c+d
3c+2d
][
−3
5
2
−3
][
1
0
0
1
]
⇒[
−6a−3b+10c+5d
−9a−6b+15c+10d
4a+3b−6c−3d
6a+4b−9c−6d
]=[
1
0
0
1
]
so, −6a−3b+10c+5d=1
4a+3b−6c−3d=0
−9a−6b+15c+10d=0
6a+4b−9c−6d=1
on squaring, we get
⇒a=
3
1
,b=1,c=
3
1
,d=
15
8
so, A=
⎣
⎢
⎢
⎡
3
1
0
3
1
15
8
⎦
⎥
⎥
⎤
=
15
1
[
5
15
5
8
].
Hence, the answer is
15
1
[
5
15
5
8
].
Step-by-step explanation:
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