Given matrix D = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of D.
Question
Given matrix D = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], find the determinant of D.
Solution
To find the determinant of a 3x3 matrix, we use the formula:
det(D) = a(ei − fh) − b(di − fg) + c(dh − eg)
where: a, b, c are the elements of the first row d, e, f are the elements of the second row g, h, i are the elements of the third row
For matrix D = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], we have:
a = 1, b = 2, c = 3 d = 0, e = 1, f = 4 g = 5, h = 6, i = 0
Substituting these values into the formula, we get:
det(D) = 1*(10 - 46) - 2*(00 - 45) + 3*(06 - 15) = 1*(-24) - 2*(-20) + 3*(-6) = -24 + 40 - 18 = -2
So, the determinant of D is -2.
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