Consider the matrix equationThe condition for existence of a non-trivial solution, and the corresponding normalised solution (up to a sign) isa)b)c)d)Correct answer is option 'D'. Can you explain this answer?

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Consider the matrix equation

The condition for existence of a non-trivial solution, and the corresponding normalised solution (up to a sign) is

Correct answer is option 'D'. Can you explain this answer?

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Consider the matrix equationThe condition for existence of a non-trivi...

For non-trivial solution, the rank of the matrix should be less than the number of variables. i.e. r < n.

For this, |A| = 0

⇒ (4c – 3b) – (2c – 6) + (b – 4) = 0

⇒ 4c – 3b – 2c + 6 + b – 4 = 0

⇒ 2c – 2b + 2 = 0

⇒ b = c + 1

The vectors x₁, x₂ ….. x_nare said to be linearly dependent, if there exist numbers λ₁, λ₂ ……. λ_n, not all zero such that

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Consider the matrix equationThe condition for existence of a non-trivial solution, and the corresponding normalised solution (up to a sign) isa)b)c)d)Correct answer is option 'D'. Can you explain this answer?

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