1 Answer
Solution :-
Given
Given that two matrices are equal.
We know that if two matrices are equal then the elements of each matrices are also equal.
Therefore by equating them we get,
3x + 4y = 2 …… (1)
x – 2y = 4 …… (2)
a + b = 5 …… (3)
2a – b = – 5 …… (4)
Multiplying equation (2) by 2 and adding to equation (1), we get
3x + 4y + 2x – 4y = 2 + 8
⇒ 5x = 10
⇒ x = 2
Now, substituting the value of x in equation (1)
3 × 2 + 4y = 2
⇒ 6 + 4y = 2
⇒ 4y = 2 – 6
⇒ 4y = – 4
⇒ y = – 1
Now by adding equation (3) and (4)
a + b + 2a – b = 5 + (– 5)
⇒ 3a = 5 – 5 = 0
⇒ a = 0
Now, again by substituting the value of a in equation (3), we get
0 + b = 5
⇒ b = 5
∴ a = 0, b = 5, x = 2 and y = – 1
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