diff --git a/guide/english/mathematics/3-by-3-determinants/index.md b/guide/english/mathematics/3-by-3-determinants/index.md index baca05e89e..3708009c40 100644 --- a/guide/english/mathematics/3-by-3-determinants/index.md +++ b/guide/english/mathematics/3-by-3-determinants/index.md @@ -31,7 +31,7 @@ Consider the following matrix, which we will call A: Then the determinant of this matrix, denoted det(A), is given by: -det(A) = a * (e * i - h * f) - b * (d * i - f * g) + c * (d * h - e * g) +
det(A) = a * (e * i - h * f) - b * (d * i - f * g) + c * (d * h - e * g)
Please keep in mind the order of operations in the expression above. @@ -57,11 +57,15 @@ For example, consider the following matrix, which we will call B: det(B) is given by the formula above. We apply the formula below: -det(B) = 1 * ( (-3) * 7 - 5 * 4) - 2 * ( 0 * 7 - 5 * (-10)) + 3 * (0 * 4 - (-3) * (-10)), which we simplify to: +
det(B) = 1 * ( (-3) * 7 - 5 * 4) - 2 * ( 0 * 7 - 5 * (-10)) + 3 * (0 * 4 - (-3) * (-10))
-det(B) = 1 * ((-21) - 20) - 2 * (0 - (-50)) + 3 * (0 - (30)), which we simplify to: +, which we simplify to: -det(B) = (-41) - 100 - 90 = -231 +
det(B) = 1 * ((-21) - 20) - 2 * (0 - (-50)) + 3 * (0 - (30))
+ +, which we simplify to: + +
det(B) = (-41) - 100 - 90 = -231
### Method 2 This method it similar to 2 by 2 determinants, and based on opertations with diagonals @@ -87,7 +91,7 @@ Again, consider the following matrix, which we will call A: Then the determinant of this matrix, denoted det(A), is given by: -det(A) = a * e * i + b * f * g + c * d * h - c * e * g - f * h * a - i * b * d +
det(A) = a * e * i + b * f * g + c * d * h - c * e * g - f * h * a - i * b * d
Note how three top-right to bottom-left diagonals are positive @@ -223,9 +227,12 @@ Consider the same example as in method 2: matrix, which we will call B: det(B) is given by the formula above. We apply the formula below: -det(B) = 1 * (-3) * 7 + 2 * 5 * (-10) + 3 * 0 * 4 - 3 * (-3) * (-10) - 5 * 4 * 1 - 7 * 2 * 0, which we simplify to: +
det(B) = 1 * (-3) * 7 + 2 * 5 * (-10) + 3 * 0 * 4 - 3 * (-3) * (-10) - 5 * 4 * 1 - 7 * 2 * 0
-det(B) = -21 - 100 + 0 - 90 - 20 - 0 = -231, same, as in method 1 +, which we simplify to: + +
det(B) = -21 - 100 + 0 - 90 - 20 - 0 = -231
+Which is the same as in method 1 #### More information: