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Computing Matrix Algebra with R and Rcpp

Challenge: Matrix Determinant

Understand how to calculate the determinant of a 3 by 3 matrix and interpret it as the volume of a parallelepiped. Practice implementing a function that performs this operation in R or Rcpp to reinforce your matrix algebra skills.

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Exercise

The determinant of a (3×3)(3 \times 3) matrix equals the volume of a parallelepiped represented by the matrix. The following illustration shows a parallelepiped where the sides are constructed using the vectors a\bf{a}, b\bf{b}, and c\bf{c}:

To calculate the parallelepiped volume, we can use the formula below.

[a1b1c1a2b2c2a3b3c3]→Determinant→a1b2c3−a1c2b3+b1c2a3−b1a2c3+c1a2c3−c1b2a3\begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{bmatrix} \to Determinant \to a_1b_2c_3 - a_1c_2b_3 + b_1c_2a_3 - b_1a_2c_3 + c_1a_2c_3 - c_1b_2a_3 ...