If matrix A
1 2 3
4 5 6
7 8 9
find
A
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Answer:
It is given that:
X[
1
4
2
5
3
6
]=[
−7
2
−8
4
−9
6
]
The matrix given on the R.H.S. of the equation is a 2×3 matrix and the one given on the L.H.S. of the equation is a 2×3 matrix.
Therefore, X has to be a 2×2 matrix.
Now, let X=[
a
b
c
d
]
Therefore, we have:
[
a
b
c
d
][
1
4
2
5
3
6
]=[
−7
2
−8
4
−9
6
]
⇒[
a+4c
b+4d
2a+5c
2b+5d
3a+6c
3b+6d
]=[
−7
2
−8
4
−9
6
]
Equating the corresponding elements of the two matrices, we have:
a+4c=−7
b+4d=2
2a+5c=−8
2b+5d=4
3a+6c=−9
3b+6d=6
Now, a+4c=−7⇒a=−7−4c
∴2a+5c=−8⇒−14−8c+5c=−8
⇒−3c=6⇒c=−2
∴a=−7−4(−2)=−7+8=1
Now, b+4d=2⇒b=2−4d
∴2b+5d=4⇒4−8d+5d=4
⇒−3d=0
⇒d=0
∴b=2−4(0)=2
Thus, a=1,b=2,c=−2,d=0
Hence, the required matrix X is [
1
2
−2
0
]
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