Mechanical Engineering > Gate 2024 > Linear Equation
Consider the system of linear equations
π‘₯ + 2𝑦 + 𝑧 = 5
2π‘₯ + π‘Žπ‘¦ + 4𝑧 = 12
2π‘₯ + 4𝑦 + 6𝑧 = 𝑏
The values of π‘Ž and 𝑏 such that there exists a non-trivial null space and the system admits infinite solutions are
A
π‘Ž = 8, 𝑏 = 14
B
π‘Ž = 4, 𝑏 = 12
C
π‘Ž = 8, 𝑏 = 12
D
π‘Ž = 4, 𝑏 = 14

Correct : a

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