Question

Let M= \(\begin{pmatrix} 1 & -1 & 0\\ -a & 2 & -1 \\0&-1&1\end{pmatrix}\)If a non-zero vector 𝑋=(𝑥, 𝑦, 𝑧)^T∈ℝ³ satisfies 𝑀⁶𝑋=𝑋, then a subspace of ℝ3 that contains the vector 𝑋 is

• A. {(𝑥, 𝑦, 𝑧)^𝑇∈ℝ³ ∶ 𝑥=0, 𝑦+𝑧=0}
• B. {(𝑥, 𝑦, 𝑧) ^𝑇∈ ℝ³ ∶𝑦 = 0, 𝑥+𝑧=0}
• C. {(𝑥, 𝑦, 𝑧) ^𝑇 ∈ ℝ³ ∶ 𝑧=0, 𝑥+𝑦=0}
• D. {(𝑥, 𝑦, 𝑧) ^𝑇 ∈ ℝ³ ∶𝑥=0, 𝑦−𝑧=0}

Answer 1

The Correct Option is B

The correct option is (B): {(𝑥, 𝑦, 𝑧) ^𝑇∈ ℝ³ ∶𝑦 = 0, 𝑥+𝑧=0}