Question

question 1 of 5
select all the correct answers.
consider the given matrix.
$a = \

$$\begin{bmatrix} 2 & \\sqrt{4} & 3^2 \\\\ 1 & 25 & 2^2 \\\\ \\sqrt{25} & 4 & 3^2 \\end{bmatrix}$$

$
which matrices are equivalent to matrix a?
$\

$$\begin{bmatrix} 2 & 2^2 & 3^2 \\\\ 1^2 & 5^2 & 2^2 \\\\ 5^2 & 2^2 & 3^2 \\end{bmatrix}$$

$
$\

$$\begin{bmatrix} 2 & 2 & 9 \\\\ 1 & 5 & 4 \\\\ 5 & 2 & 9 \\end{bmatrix}$$

$
$\

$$\begin{bmatrix} 2 & 2 & 9 \\\\ 1 & 25 & 4 \\\\ 5 & 4 & 9 \\end{bmatrix}$$

$
$\

$$\begin{bmatrix} 2 & 2 & 9 \\\\ 1 & 5^2 & 2^2 \\\\ 5 & 2^2 & 3^2 \\end{bmatrix}$$

$

Explanation:

Step1: Simplify matrix A entries

Calculate each value in matrix $A$:
$\sqrt{4}=2$, $3^2=9$, $2^2=4$, $\sqrt{25}=5$
So $A =

$$\begin{bmatrix} 2 & 2 & 9 \\ 1 & 25 & 4 \\ 5 & 4 & 9 \end{bmatrix}$$

$

Step2: Check first option matrix

Simplify its entries: $2^2=4$, $1^2=1$, $5^2=25$
Result:

$$\begin{bmatrix} 2 & 4 & 9 \\ 1 & 25 & 4 \\ 25 & 4 & 9 \end{bmatrix}$$

(not equal to $A$)

Step3: Check second option matrix

Matrix:

$$\begin{bmatrix} 2 & 2 & 9 \\ 1 & 5 & 4 \\ 5 & 2 & 9 \end{bmatrix}$$

(entries 25→5, 4→2 differ from $A$)

Step4: Check third option matrix

Matrix:

$$\begin{bmatrix} 2 & 2 & 9 \\ 1 & 25 & 4 \\ 5 & 4 & 9 \end{bmatrix}$$

(matches simplified $A$)

Step5: Check fourth option matrix

Simplify its entries: $5^2=25$, $2^2=4$, $3^2=9$
Result:

$$\begin{bmatrix} 2 & 2 & 9 \\ 1 & 25 & 4 \\ 5 & 4 & 9 \end{bmatrix}$$

(matches simplified $A$)

Answer:

$$\begin{bmatrix} 2 & 2 & 9 \\ 1 & 25 & 4 \\ 5 & 4 & 9 \end{bmatrix}$$

,

$$\begin{bmatrix} 2 & 2 & 9 \\ 1 & 5^2 & 2^2 \\ 5 & 2^2 & 3^2 \end{bmatrix}$$