QQuestionMathematics
QuestionMathematics
Which expression is equivalent to
\left(\begin{array}{cc}
\frac{5}{4} & \frac{1}{4} \\
\frac{4}{4} & \cdot 4 \\
\frac{1}{4}
\end{array}\right)^{1}
\begin{aligned}
& \text { ○ } 15 \sqrt{4} \\
& \text { ○ } \sqrt{2^{5}} \\
& \text { ○ } 2 \\
& \text { ○ } 4
\end{aligned}
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the Matrix
\frac{1}{4}
The given matrix is: \end{array}\right)^{1}
Step 3:: Simplify the Matrix Elements
- Fifth element: $$\frac{1}{4}$$ (already simplified)
- Second element: \frac{1}{4} (already simplified)
Step 4:: Understand the Exponent
The matrix is raised to the power of 1, which means it remains unchanged.
Step 5:: Evaluate the Options
- $$4
Looking at the given options:
Step 6:: Analyze the Matrix
The matrix doesn't directly correspond to any of these values.
Step 7:: Simplify \sqrt{2^{5}}
\sqrt{2^{5}} = 2^{\frac{5}{2}} = 2^{2.5} = 4\sqrt{2}
Final Answer
The correct answer is 4, which matches the fourth element of the matrix when simplified.
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