Answer to Question #236806 in Linear Algebra for moe

Question #236806

Find all real values of λ such that 

"\\left| \\begin{array}{cccc}1 & \\lambda & -1\\\\ 1 & -1 & -\\lambda \\\\ \\lambda & -1 & 1\\end{array} \\right |=0."


  1. λ=0
  2. "\\lambda=\\sqrt{3}"
  3. "\\lambda=-\\sqrt{3}"
  4. There is no such λ
  5. λ=1
1
Expert's answer
2021-09-16T17:52:52-0400
"\\begin{vmatrix}\n 1 & \\lambda & -1 \\\\\n 1 & -1 & -\\lambda \\\\\n \\lambda & -1 & 1 \\\\\n\\end{vmatrix}=1\\begin{vmatrix}\n -1 & -\\lambda \\\\\n -1 & 1\n\\end{vmatrix}-\\lambda\\begin{vmatrix}\n 1 & -\\lambda \\\\\n \\lambda & 1\n\\end{vmatrix}-1\\begin{vmatrix}\n 1 & -1 \\\\\n \\lambda & -1\n\\end{vmatrix}"

"=-1-\\lambda-\\lambda-\\lambda^2+1-\\lambda=-\\lambda^2-3\\lambda=0"


"-\\lambda(\\lambda+3)=0"

"\\lambda_1=-3, \\lambda_2=0"

1. "\\lambda=0"



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