↪ To calculate the determinant of the 3x3 matrix:
| 4 1 6 |
| 3 0 2 |
| 5 8 7 |
You can use the following formula for a 3x3 matrix:
det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)
Where the matrix is:
| a b c |
| d e f |
| g h i |
In your case:
a = 4, b = 1, c = 6
d = 3, e = 0, f = 2
g = 5, h = 8, i = 7
Now, plug these values into the formula:
det(A) = 4(0*7 - 2*8) - 1(3*7 - 2*5) + 6(3*8 - 0*5)
Calculate the individual products and differences:
det(A) = 4(-16) - 1(21 - 10) + 6(24 - 0)
Now, perform the calculations:
det(A) = -64 - 1(11) + 6(24)
det(A) = -64 - 11 + 144
Finally, add the numbers together to find the determinant:
det(A) = -64 - 11 + 144 = 69
So, the determinant of the matrix is 69.
