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Answers
Answer:
5
Step-by-step explanation:
Given ,
AB = BA
To Find :-
Value of 'x'
Solution :-
Finding value of 'AB' :-
Multiplying 1st row in 'A' with 1st column in 'B' :-
= (2 × 1) + (x × 0)
= 2 + 0
= 2
[ ∴ '2' will be in the 1st row 1st column in matrix 'AB' ]
Multiplying 1st row in 'A' with '2'nd column in 'B' :-
= (2 × 4) + (x × (-1) )
= 8 - x
[ ∴ '8 - x' will be in the 1st row 2nd column in the matrix 'AB' ]
Multiplying 2nd row in 'A' with '1'st column in 'B' :-
= (0 × 1) + (-1/2 × 0)
= 0 + 0
= 0
[ ∴ '0' will be in the 2nd row , 1st column in the matrix 'AB' ]
Multiplying 2nd row in 'A' with 2nd column in 'B' :-
= (0 × 4) + (-1/2 × - 1)
= 0 + 1/2
= 1/2
[ ∴ 1/2 will be in the 2nd row , 2nd column in 'AB' ]
Finding value of 'BA' :-
Multiplying 1st row in 'B' with 1st column in 'A' :-
= (1 × 2) + (4 × 0)
= 2 + 0
= 2
[ ∴ '2' will be in the 1st row 1st column in matrix 'BA' ]
Multiplying 1st row in 'B' with '2'nd column in 'A' :-
= (1 × x) + (4 × -1/2 )
= x + (-2)
= x - 2
[ ∴ 'x - 2' will be in the 1st row 2nd column in the matrix 'BA' ]
Multiplying 2nd row in 'B' with '1'st column in 'A' :-
= (0 × 2) + (-1 × 0)
= 0 + 0
= 0
[ ∴ '0' will be in the 2nd row , 1st column in the matrix 'BA' ]
Multiplying 2nd row in 'B' with 2nd column in 'A' :-
= (0 × x) + (-1 × -1/2)
= 0 + 1/2
= 1/2
[ ∴ '0' will be in the 2nd row , 1st column in the matrix 'BA' ]
AB = BA
We can see that all terms are equal expect '1' , So we equating those both terms :-
8 - x = x - 2
8 + 2 = x + x
10 = 2x
x = 10/2
x = 5
∴ Value of 'x' = 5
Answer :-
Value of x is 5.
Step-by-step explanation :-
Given :
If A = , B = , find x if AB = BA ?
Solution :
AB =
AB =
AB =
∴ AB =
________________________________
BA =
BA =
BA =
∴ BA =
________________________________
Now, AB = BA
=
So, [8 - x] = [x - 2]
⇒ 8 + 2 = x + x
⇒ 10 = 2x
⇒ x = 10/2
∴ x = 5