Select the correct option from the given alternatives: The system 3x – y + 4z = 3, x + 2y –3z = –2 and 6x + 5y + λz = –3 has at least one Solution when - Mathematics and Statistics

प्रश्न

Select the correct option from the given alternatives:

The system 3x – y + 4z = 3, x + 2y – 3z = –2 and 6x + 5y + λz = –3 has at least one Solution when

विकल्प

λ = –5
λ = 5
λ = 3
λ = –13

MCQ

उत्तर

λ = –5

Explanation:

The given system of equations will have more than one solution if

$| \begin{matrix} 3 & - 1 & 4 \\ 1 & 2 & - 3 \\ 6 & 5 & λ \end{matrix} |$ = 0

Applying R₃ → R₃– (R₁ + 3R₂), we get

$| \begin{matrix} 3 & - 1 & 4 \\ 1 & 2 & - 3 \\ 0 & 0 & λ + 5 \end{matrix} |$ = 0

∴ 3[2(λ + 5) – 0] – (–1) (λ + 5 – 0) + 4(0 – 0) = 0

∴ 7λ + 35 = 0

∴ λ = $- \frac{35}{7}$

= – 5

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Properties of Determinants

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q I. (6)Q I. (5)Q I. (7)

अध्याय 4: Determinants and Matrices - Miscellaneous Exercise 4(A) [पृष्ठ ७६]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board

अध्याय 4 Determinants and Matrices
Miscellaneous Exercise 4(A) | Q I. (6) | पृष्ठ ७६

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Select the correct option from the given alternatives: The system 3x – y + 4z = 3, x + 2y –3z = –2 and 6x + 5y + λz = –3 has at least one Solution when - Mathematics and Statistics

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Select the correct option from the given alternatives: The system 3x – y + 4z = 3, x + 2y –3z = –2 and 6x + 5y + λz = –3 has at least one Solution when - Mathematics and Statistics

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