The sum of distinct values of λ for which the system of equations
(λ – 1)x + (3λ + 1)y + 2λz = 0
(λ – 1)x + (4λ – 2)y + (λ + 3)z = 0
2x + (3λ + 1)y + 3(λ – 1)z = 0,
has non-zero solutions, is
The sum of distinct values of λ for which the system of equations
(λ – 1)x + (3λ + 1)y + 2λz = 0
(λ – 1)x + (4λ – 2)y + (λ + 3)z = 0
2x + (3λ + 1)y + 3(λ – 1)z = 0,
has non-zero solutions, is
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1 Answer
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|λ-1 3λ+1 2λ|
|λ-1 4λ-2 λ+3| = 0
|2 3λ+1 3 (λ-1)|
R? → R? - R? and R? → R? - R? (from a similar matrix setup, applying operations to simplify)
The provided solution uses a slightly different matrix but let's follow the subsequent steps.
A different matrix from the image is used in the calculation:
|λ-1 3λ+1 2λ|
|0 λ-3 -λ+3|
|3-λ 0 λ-3 |
C? → C? + C?
|3λ-1 3λ+1 2λ |
|3-λ λ-3-λ | = 0
|0 λ-3 |
⇒ (λ-3) [ (3λ-1) (λ-3) - (3λ+1) (3-λ)] = 0
⇒ (&l...more
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