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:

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

$$ \text{Invertible} \implies \text{Square Matrix} \quad (\text{Rows} = \text{Columns}) $$

$$ 3 e 2 \implies \text{Not Square} \implies \text{Not Invertible} $$

Answer:

• Yes, it is a square matrix
• No, it is not a square matrix (Correct answer)