Question

20. Consider the following matrix over \( \mathbb{R} \) : \[ M=\left[\begin{array}{rrc} \lambda & 0 & 6 \\ -1 & \lambda & -5 \\ 0 & -1 & \lambda-2 \end{array}\right] \] Working over \( \mathbb{R} \), find all real numbers \( \lambda \) such that \( M \) is not invertible. \( \lambda=-1, \lambda=2 \) and \( \lambda=3 \) \( \lambda=1, \lambda=-2 \) and \( \lambda=3 \) \( \lambda=1, \lambda=2 \) and \( \lambda=-3 \) \( \lambda=0, \lambda=1 \) and \( \lambda=2 \) \( \lambda=1, \lambda=2 \) and \( \lambda=3 \)

          20. Consider the following matrix over \( \mathbb{R} \) :
\[
M=\left[\begin{array}{rrc}
\lambda & 0 & 6 \\
-1 & \lambda & -5 \\
0 & -1 & \lambda-2
\end{array}\right]
\]

Working over \( \mathbb{R} \), find all real numbers \( \lambda \) such that \( M \) is not invertible.
\( \lambda=-1, \lambda=2 \) and \( \lambda=3 \)
\( \lambda=1, \lambda=-2 \) and \( \lambda=3 \)
\( \lambda=1, \lambda=2 \) and \( \lambda=-3 \)
\( \lambda=0, \lambda=1 \) and \( \lambda=2 \)
\( \lambda=1, \lambda=2 \) and \( \lambda=3 \)

20. Consider the following matrix over ℝ :

M=[
λ 0 6

-1 λ -5

0 -1 λ-2
]

Working over ℝ, find all real numbers λ such that M is not invertible.
λ=-1, λ=2 and λ=3
λ=1, λ=-2 and λ=3
λ=1, λ=2 and λ=-3
λ=0, λ=1 and λ=2
λ=1, λ=2 and λ=3

Added by Randy R.

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