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Answer:

Step-by-step explanation:

Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble? Daniel has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. What is the probability that he will draw a green marble?

To find the determinants of matrices related to \( A \), we can use properties of determinants. Let's denote the rows of matrix \( A \) as \( v_1, v_2, v_3, \) and \( v_4 \).

1. Determinant of \( 2A \):
Since \( 2A \) means multiplying each element of \( A \) by 2, the determinant of \( 2A \) will be \( (2^4) \) times the determinant of \( A \).
\[ \text{det}(2A) = (2^4) \cdot \text{det}(A) = 16 \cdot 6 = 96 \]

2. Determinant of \( A^T \):
The determinant of the transpose of a matrix is equal to the determinant of the original matrix.
\[ \text{det}(A^T) = \text{det}(A) = 6 \]

3. Determinant of \( A^{-1} \):
The determinant of the inverse of a matrix \( A \) is equal to the reciprocal of the determinant of \( A \).
\[ \text{det}(A^{-1}) = \frac{1}{\text{det}(A)} = \frac{1}{6} \]

4. Determinant of \( A^2 \):
The determinant of the square of a matrix \( A \) is equal to the determinant of \( A \) raised to the power of 2.
\[ \text{det}(A^2) = (\text{det}(A))^2 = 6^2 = 36 \]

These are the determinants of the matrices related to \( A \).


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