1. The problem asks to find which matrices among A, B, C, and D are equivalent. 2. Two matrices are equivalent if they have the same dimensions and the same corresponding elements. 3. Let's write down each matrix clearly: $$A = \begin{bmatrix} \sqrt{2} & 1 \\ 1 & \sqrt{2} \\ \sqrt{2} & 1 \end{bmatrix}$$ $$B = \begin{bmatrix} 2 & 1 & 2 \\ 1 & 2 & 1 \end{bmatrix}$$ $$C = \begin{bmatrix} 2 & 1 \\ 1 & 2 \\ 2 & 1 \end{bmatrix}$$ $$D = \begin{bmatrix} \sqrt{4} & 1 \\ 1 & \sqrt{4} \\ \sqrt{4} & 1 \end{bmatrix}$$ 4. Check dimensions: - A is 3x2 - B is 2x3 - C is 3x2 - D is 3x2 5. Since B is 2x3, it cannot be equivalent to A, C, or D which are 3x2. 6. Now compare A, C, and D element-wise: - Note that $\sqrt{4} = 2$. Matrix A: $$\begin{bmatrix} \sqrt{2} & 1 \\ 1 & \sqrt{2} \\ \sqrt{2} & 1 \end{bmatrix}$$ Matrix C: $$\begin{bmatrix} 2 & 1 \\ 1 & 2 \\ 2 & 1 \end{bmatrix}$$ Matrix D: $$\begin{bmatrix} 2 & 1 \\ 1 & 2 \\ 2 & 1 \end{bmatrix}$$ 7. Since $\sqrt{2} \approx 1.414$ and $2$ is different, A is not equivalent to C or D. 8. Matrices C and D are identical. **Final answer:** The equivalent matrices are C and D.