Given
2 11
X =
3 4
x= []
write:
(1) the order of the matrix X
(ii) the matrix X
Answers
Answered by
6
Step-by-step explanation:
Here, AX=B, where A=[
2
−3
1
4
] and B=[
7
6
]
(i) The order of A is 2×2 and order of B is 2×1. Let the order of X be m×n.
Now, AX will exist only if the number of columns of A is equal to the number of rows of X, i.e, m=2
When a matrix of order a×c is multiplied with another matrix of order c×b, the resultant matrix has the order a×b.
A
2×2
×X
2×n
=(AX)
2×n
=B
2×1
∴n=1
Therefore, order of matrix X is 2×1
(ii) Let X=[
a
b
]
[
2
−3
1
4
][
a
b
]=[
7
6
]
⇒[
2a+b
−3a+4b
]=[
7
6
]
Therefore,
2a+b=7...(1)
−3a+4b=6...(2)
From (1), we get b=7−2a. Substitute this value of in (2).
−3a+4(7−2a)=6
⇒−3a+28−8a=6⇒11a=22⇒a=2
b=7−2a=7−2(2)=3
∴X=[
2
3
]
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