Find the determinant of the matrix: | 1 2 | | 3 5 |.

1 question

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Q: Find the determinant of the matrix: | 1 2 | | 3 5 |.

Solution: det = (1*5) - (2*3) = 5 - 6 = -1.

Steps: 8

Step 1: Identify the elements of the 2x2 matrix. The matrix is: | 1 2 | | 3 5 |.
Step 2: Label the elements of the matrix. Let a = 1, b = 2, c = 3, d = 5.
Step 3: Use the formula for the determinant of a 2x2 matrix, which is: det = (a * d) - (b * c).
Step 4: Substitute the values into the formula: det = (1 * 5) - (2 * 3).
Step 5: Calculate the first part: 1 * 5 = 5.
Step 6: Calculate the second part: 2 * 3 = 6.
Step 7: Subtract the second part from the first part: 5 - 6 = -1.
Step 8: The determinant of the matrix is -1.