What is the determinant of the matrix: | 1 2 3 | | 4 5 6 | | 7 8 10 |?

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Q: What is the determinant of the matrix: | 1 2 3 | | 4 5 6 | | 7 8 10 |?

Solution: Calculating gives a determinant of -3.

Steps: 10

Step 1: Write down the matrix: | 1 2 3 | | 4 5 6 | | 7 8 10 |.
Step 2: Identify the elements of the matrix: a = 1, b = 2, c = 3, d = 4, e = 5, f = 6, g = 7, h = 8, i = 10.
Step 3: Use the formula for the determinant of a 3x3 matrix: det(A) = a(ei - fh) - b(di - fg) + c(dh - eg).
Step 4: Calculate ei - fh: (5 * 10) - (6 * 8) = 50 - 48 = 2.
Step 5: Calculate di - fg: (4 * 10) - (6 * 7) = 40 - 42 = -2.
Step 6: Calculate dh - eg: (4 * 8) - (5 * 7) = 32 - 35 = -3.
Step 7: Substitute these values into the determinant formula: det(A) = 1 * 2 - 2 * (-2) + 3 * (-3).
Step 8: Calculate: 1 * 2 = 2, -2 * -2 = 4, 3 * -3 = -9.
Step 9: Combine these results: 2 + 4 - 9 = -3.
Step 10: The determinant of the matrix is -3.