Calculate the determinant of the matrix \( B = \begin{pmatrix} 2 & 3 \\ 5 &a

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Question: Calculate the determinant of the matrix \\( B = \\begin{pmatrix} 2 & 3 \\\\ 5 & 7 \\end{pmatrix} \\).

Options:

Correct Answer: 10

Solution:

The determinant is calculated as \\( 2*7 - 3*5 = 14 - 15 = -1 \\).

Calculate the determinant of the matrix \( B = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).

Calculate the determinant of the matrix \( B = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).

Step 1: Identify the elements of the matrix B. The matrix B is given as B = [[2, 3], [5, 7]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is: det(B) = (a * d) - (b * c), where a, b, c, and d are the elements of the matrix.
Step 3: Assign the values from the matrix to the variables in the formula. Here, a = 2, b = 3, c = 5, and d = 7.
Step 4: Substitute the values into the formula. This gives us: det(B) = (2 * 7) - (3 * 5).
Step 5: Calculate the products. First, calculate 2 * 7 = 14. Then, calculate 3 * 5 = 15.
Step 6: Subtract the second product from the first. So, 14 - 15 = -1.
Step 7: Write down the final result. The determinant of the matrix B is -1.

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