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If the system of equations 3x-2y+z=0, x-14y+15z=0,x+2y-3z=0 ha

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If the system of equations $3 x - 2 y + z = 0, λ x - 14 y + 15 z = 0, x + 2 y - 3 z = 0$ have non zero solution, then find $λ$

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If the system of equations

3 x - 2 y + z = 0, λ x - 14 y + 15 z = 0, x + 2 y - 3 z = 0

have non zero solution, then find

λ

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Text solutionVerified

Given

3 x - 2 y + z = 0 \to 1

λ x - 14 y + 15 z = 0 \to 2

x + 2 y - 3 z = 0 \to 3

So, by forming a matrix we get

⎣ ⎡ 3 λ 1 - 2 - 14 2 115 - 3 ⎦ ⎤ = 0

Taking the determinant of above matrix,

3 (42 - 30) + 2 (- 3 λ - 15) + 1 (2 λ + 14) = 0

3 (12) + 2 (- 3 λ - 15) + 1 (2 λ + 14) = 0

36 - 6 λ - 30 + 2 λ + 14 = 0

20 - 4 λ = 0

λ = 5

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Question Text	If the system of equations $3 x - 2 y + z = 0, λ x - 14 y + 15 z = 0, x + 2 y - 3 z = 0$ have non zero solution, then find $λ$
Answer Type	Text solution:1
Upvotes	150