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प्रश्न
Examine the consistency of the following equation:
x + 2y −3 = 0, 7x + 4y − 11 = 0, 2x + 4y − 6 = 0
उत्तर
The given equations are
x + 2y −3 = 0,
7x + 4y − 11 = 0,
2x + 4y − 6 = 0
These equations are consistent, if
`|(1, 2, -3),(7, 4, -11),(2, 4, -6)| = 0, "provided" |(1, 2),(7, 4)| ` ≠ 0 which is obviously true.
Now, L.H.S. = `|(1, 2, -3),(7, 4, -11),(2, 4, -6)|`
= 1(–24 + 44) – 2(–42 + 22) – 3(28 – 8)
= 1(20) – 2(–20) – 3(20)
= 20 + 40 – 60
= 0
= R.H.S.
∴ The given equations are consistent.
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