(35S) Determinant and Cramer's Rule for 3 x 3 Matrices - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: General Software Library (/forum-13.html) +--- Thread: (35S) Determinant and Cramer's Rule for 3 x 3 Matrices (/thread-13964.html) |
(35S) Determinant and Cramer's Rule for 3 x 3 Matrices - Eddie W. Shore - 11-09-2019 03:31 PM Blog Link: http://edspi31415.blogspot.com/2019/11/hp-35s-determinant-and-cramers-rule-3-x.html Determinant of a 3 x 3 Matrix The following program calculates a determinant of a matrix: [ [ K, N, Q ] [ L, O, R ] [ M, P, S ] ] The determinant is K*O*S + N*R*M + Q*L*P - M*O*Q - P*R*K - S*L*N. Enter the elements in columns. Program HP 35S: Determinant Code: D001 LBL D Examples: [ [ -3, 3, 2 ] [ 5, 4, -1 ] [ 2, 1, 4 ] ] Determinant: -123 [ [ 5, 0, 7 ] [ -2, 4, -1 ] [ -3, 11, 6 ] ] Determinant: 105 Cramer's Rule Cramer's Rule solves the linear system: [[ A, D, G ] [[ x ] = [[ X ] [ B, E, H ] [ y ] = [ Y ] [ C, F, I ]] [ z ]] = [ Z ]] x = U, y = V, z = W, T = determinant of the coefficients Program HP 35S: Cramer's Rule Code: C001 LBL C Examples: [[ -3, 2, -4 ] [[ x ] = [[ 0 ] [ 6, 1, 2 ] [ y ] = [ 2 ] [ 3, 3, 7 ]] [ z ]] = [ 6 ]] T: -135 x ≈ 0.0296 y ≈ 0.9333 z ≈ 0.4444 [[ 0, 10, 6 ] [[ x ] = [[ 3 ] [ 5, 3, 8 ] [ y ] = [ 6.5 ] [ -5, 8, 2 ]] [ z ]] = [ 7 ]] T: -830 x ≈ -0.0843 y ≈ 0.6687 z ≈ 0.6145 Source: Pike, Scott. "Using Cramer's Rule to Solve Three Equations with Three Unknowns" Mesa Community College. http://www.mesacc.edu/~scotz47781/mat150/notes/cramers_rule/Cramers_Rule_3_by_3_Notes.pdf Retrieved September 24, 2019 |