Let \( A=\left[\begin{array}{ll}7 & 9 \\ 4 & 1\end{array}\right] \). Write 2A. Is \( \operatorname{det}(2 A) \) equal to \( 2 \operatorname{det}(A) ? \) \( 2 A=\square \) (Type an integer or decimal for each matrix element.)

To find \( 2A \), we multiply each element of matrix \( A \) by 2: \[ 2A = 2 \cdot \left[\begin{array}{ll}7 & 9 \\ 4 & 1\end{array}\right] = \left[\begin{array}{ll}2 \cdot 7 & 2 \cdot 9 \\ 2 \cdot 4 & 2 \cdot 1\end{array}\right] = \left[\begin{array}{ll}14 & 18 \\ 8 & 2\end{array}\right] \] Now, let's calculate \( \operatorname{det}(A) \): \[ \operatorname{det}(A) = (7)(1) - (9)(4) = 7 - 36 = -29 \] Next, we find \( \operatorname{det}(2A) \): \[ \operatorname{det}(2A) = \operatorname{det}\left(\left[\begin{array}{ll}14 & 18 \\ 8 & 2\end{array}\right]\right) = (14)(2) - (18)(8) = 28 - 144 = -116 \] Finally, we calculate \( 2 \operatorname{det}(A) \): \[ 2 \operatorname{det}(A) = 2 \cdot (-29) = -58 \] Now we can compare \( \operatorname{det}(2A) \) and \( 2 \operatorname{det}(A) \): \[ \operatorname{det}(2A) = -116 \quad \text{and} \quad 2 \operatorname{det}(A) = -58 \] Thus, \[ \operatorname{det}(2A) \neq 2 \operatorname{det}(A) \] In conclusion, \( 2 A=\left[\begin{array}{ll}14 & 18 \\ 8 & 2\end{array}\right] \) and \( \operatorname{det}(2 A) \) is not equal to \( 2 \operatorname{det}(A) \).