Question

question 25 points 1

is the matrix \\(\

$$\begin{bmatrix} 1 & 2 \\\\ 5 & 4 \\\\ 3 & 7 \\end{bmatrix}$$

\\) invertible? why or why not?

• yes, it is a square matrix
• no, it is not a square matrix

Explanation:

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<reasoning>

Determine the matrix dimensions

Using the Matrix Dimensions knowledge point
\[
\text{Rows} = 3,\quad \text{Columns} = 2
\]
\[
\text{Dimensions} = 3 \times 2
\]

Apply invertibility condition

Using the Matrix Inverse Existence knowledge point
\[
\text{Invertible} \implies \text{Square Matrix} \quad (\text{Rows} = \text{Columns})
\]
\[
3
e 2 \implies \text{Not Square} \implies \text{Not Invertible}
\]
</reasoning>

<answer>
<mcq-option>Yes, it is a square matrix</mcq-option>
<mcq-correct>No, it is not a square matrix</mcq-correct>
</answer>

<post_analysis>
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Answer:

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<reasoning>

Determine the matrix dimensions

Using the Matrix Dimensions knowledge point
\[
\text{Rows} = 3,\quad \text{Columns} = 2
\]
\[
\text{Dimensions} = 3 \times 2
\]

Apply invertibility condition

Using the Matrix Inverse Existence knowledge point
\[
\text{Invertible} \implies \text{Square Matrix} \quad (\text{Rows} = \text{Columns})
\]
\[
3
e 2 \implies \text{Not Square} \implies \text{Not Invertible}
\]
</reasoning>

<answer>
<mcq-option>Yes, it is a square matrix</mcq-option>
<mcq-correct>No, it is not a square matrix</mcq-correct>
</answer>

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