Calculate the determinant of a matrix A = [2 -1 3; 0 1 4; -2 0 5]
Question
Calculate the determinant of a matrix A = [2 -1 3; 0 1 4; -2 0 5]
Solution
To calculate the determinant of a 3x3 matrix, we use the formula:
det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)
where: a, b, c are the entries of the first row d, e, f are the entries of the second row g, h, i are the entries of the third row
For the given matrix A = [2 -1 3; 0 1 4; -2 0 5], the entries are:
a = 2, b = -1, c = 3 d = 0, e = 1, f = 4 g = -2, h = 0, i = 5
Substituting these into the formula gives:
det(A) = 2(15 - 40) - (-1)(05 - 4-2) + 3(00 - 1-2) = 25 - 18 + 3*2 = 10 - 8 + 6 = 8
So, the determinant of the matrix A is 8.
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