Det Calculator

Square matrix. Rows separated by a semicolon or newline, entries by spaces or commas.
Determinant
-306
Matrix Determinant Calculator
Order (n)
3
Singular (det = 0)
no
Invertible
yes
Rank
3
Trace
11
Method used
Cofactor / Laplace expansion along the first row
Expansion
(6)(-54) + (1)(-18) + (1)(36) = -306
Matrix
6 1 1; 4 -2 5; 2 8 7
Worked out from Gilbert Strang, Introduction to Linear Algebra, ch. 5 (determinants) and 1 other source.

How this is worked out

8 steps
  1. Matrix is 3x3.
  2. [ 6 1 1 ]
  3. [ 4 -2 5 ]
  4. [ 2 8 7 ]
  5. Minor M(1,1) = -54, cofactor C(1,1) = -54.
  6. Minor M(1,2) = 18, cofactor C(1,2) = -18.
  7. Minor M(1,3) = 36, cofactor C(1,3) = 36.
  8. Expanding along row 1: det = (6)(-54) + (1)(-18) + (1)(36) = -306

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