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प्रश्न
Examine the consistency of the following equation:
2x − y + 3 = 0, 3x + y − 2 = 0, 11x + 2y − 3 = 0
उत्तर
The given equations are
2x – y = –3
3x + y = 2
11x + 2y =3
These equations are consistent, if
`|(2, -1, -3),(3, 1, 2),(11, 2, 3)| = 0, "provided" |(2, -1),(3, 1)| ` ≠ 0 which is obviously true.
Now, L.H.S. `|(2, -1, -3),(3, 1, 2),(11, 2, 3)|`
= 2(3 – 4) + 1(9 – 22) – 3(6 – 11)
= – 2 – 13 + 15
= 0
= R.H.S.
∴ the given equations are consistent.
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