Question

Question 2 Consider the following real matrices: \[ \begin{array}{l} \mathbf{u}:=\left[\begin{array}{c} 2 \\ 0 \\ -1 \end{array}\right] \\ \mathbf{v}=\left[\begin{array}{c} 0 \\ 1 \\ -1 \end{array}\right] \\ A:=\left[\begin{array}{ccc} -1 & 0 & 2 \\ 0 & 2 & 1 \end{array}\right] \\ B:=\left[\begin{array}{ll} 0 & 1 \\ 2 & 0 \end{array}\right] \end{array} \] Select all of the following statements which are TRUE. \( B^{2}=2 I \) \( A^{\top} B^{\top}=(B A)^{\top} \) \( \mathbf{v u}^{\top}=\mathbf{u v}^{\top} \) \( B^{2}=0 \) \( A^{\top} B=B^{\top} A \) \( A^{\top} B \) is undefined \( \mathbf{u v}^{\top} \) is undefined \( \mathbf{u}^{\top} \mathbf{v}=\mathbf{v}^{\top} \mathbf{u} \) \( A B^{\top} \) is undefined

          Question 2

Consider the following real matrices:
\[
\begin{array}{l}
\mathbf{u}:=\left[\begin{array}{c}
2 \\
0 \\
-1
\end{array}\right] \\
\mathbf{v}=\left[\begin{array}{c}
0 \\
1 \\
-1
\end{array}\right] \\
A:=\left[\begin{array}{ccc}
-1 & 0 & 2 \\
0 & 2 & 1
\end{array}\right] \\
B:=\left[\begin{array}{ll}
0 & 1 \\
2 & 0
\end{array}\right]
\end{array}
\]

Select all of the following statements which are TRUE.
\( B^{2}=2 I \)
\( A^{\top} B^{\top}=(B A)^{\top} \)
\( \mathbf{v u}^{\top}=\mathbf{u v}^{\top} \)
\( B^{2}=0 \)
\( A^{\top} B=B^{\top} A \)
\( A^{\top} B \) is undefined
\( \mathbf{u v}^{\top} \) is undefined
\( \mathbf{u}^{\top} \mathbf{v}=\mathbf{v}^{\top} \mathbf{u} \)
\( A B^{\top} \) is undefined

Question 2

Consider the following real matrices:

𝐮:=[
2

0

-1
]
𝐯=[
0

1

-1
]

A:=[
-1 0 2

0 2 1
]

B:=[
0 1

2 0
]

Select all of the following statements which are TRUE.
B^2=2 I
A^⊤ B^⊤=(B A)^⊤
𝐯 𝐮^⊤=𝐮 𝐯^⊤
B^2=0
A^⊤ B=B^⊤ A
A^⊤ B is undefined
𝐮 𝐯^⊤ is undefined
𝐮^⊤𝐯=𝐯^⊤𝐮
A B^⊤ is undefined

Added by Tina L.

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