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

Answer: (B)

{(𝑥, 𝑦, 𝑧) 𝑇∈ ℝ3 ∶𝑦 = 0, 𝑥+𝑧=0}

Answer 2

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