Question

5
select the correct answer from the drop-down menu.
$a = \

$$\begin{bmatrix} \\sqrt{2} & 1 \\\\ 1 & \\sqrt{2} \\\\ \\sqrt{2} & 1 \\end{bmatrix}$$

$ $b = \

$$\begin{bmatrix} 2 & 1 & 2 \\\\ 1 & 2 & 1 \\end{bmatrix}$$

$ $c = \

$$\begin{bmatrix} 2 & 1 \\\\ 1 & 2 \\\\ 2 & 1 \\end{bmatrix}$$

$ $d = \

$$\begin{bmatrix} \\sqrt{4} & 1 \\\\ 1 & \\sqrt{4} \\\\ \\sqrt{4} & 1 \\end{bmatrix}$$

$
the equivalent matrices are $\boldsymbol{\
abla}$

Explanation:

Step1: Simplify matrix D entries

Since $\sqrt{4}=2$, rewrite matrix $D$:

$$D =
LATEXBLOCK1
$$

Step2: Compare matrices to find matches

Compare simplified $D$ to matrix $B$:

$$B =
LATEXBLOCK2
$$

Transpose of $B$ is

$$\begin{bmatrix} 2 & 1 \\ 1 & 2 \\ 2 & 1 \end{bmatrix}$$

, which equals $D$. Matrices that are transposes (or can be transformed via row/column swaps/scaling that preserves equivalence) are equivalent.

Answer:

$B$ and $D$