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प्रश्न
Answer the following question:
Find the value of k, if the following equations are consistent:
(k + 1)x + (k – 1)y + (k – 1) = 0
(k – 1)x + (k + 1)y + (k – 1) = 0
(k – 1)x + (k – 1)y + (k + 1) = 0
उत्तर
Given equations are
(k + 1)x + (k – 1)y + (k – 1) = 0
(k – 1)x + (k + 1)y + (k – 1) = 0
(k – 1)x + (k – 1)y + (k + 1) = 0
Since these equations are consistent,
`|("k" + 1, "k" - 1, "k" - 1),("k" - 1, "k" + 1, "k" - 1),("k" - 1, "k" - 1, "k" + 1)|` = 0
Applying C1 → C1 – C2, we get
`|(2, "k" - 1, "k" - 1),(-2, "k" + 1, "k" - 1),(0, "k" - 1, "k" + 1)|` = 0
Applying C2 → C2 – C3, we get
`|(2, 0, "k" - 1),(-2, 2, "k" - 1),(0, -2, "k" + 1)|` = 0
∴ 2(2k + 2 + 2k – 2) – 0 + (k – 1) (4 – 0) = 0
∴ 2(4k) + (k – 1) 4 = 0
∴ 8k + 4k – 4 = 0
∴ 12k – 4 = 0
∴ k = `4/12`
= `1/3`
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