1 files changed, 47 insertions, 0 deletions
diff --git a/3293/CH3/EX3.24/Ex3_24.sce b/3293/CH3/EX3.24/Ex3_24.sce
new file mode 100755
index 000000000..4e486903f
--- /dev/null
+++ b/3293/CH3/EX3.24/Ex3_24.sce
@@ -0,0 +1,47 @@
+//page 104
+//Example 3.24
+clc;
+clear;
+close;
+disp('W be the subspace of R^5 spanned by vectors:');
+a1 = [2 -2 3 4 -1];
+a2 = [-1 1 2 5 2];
+a3 = [0 0 -1 -2 3];
+a4 = [1 -1 2 3 0];
+disp(a1,'a1 = ');
+disp(a2,'a2 = ');
+disp(a3,'a3 = ');
+disp(a4,'a4 = ');
+disp('Matrix A by the row vectors a1,a2,a3,a4 will be:');
+A = [a1;a2;a3;a4];
+disp(A,'A = ');
+disp('After Applying row transformations, we get the row reduced echelon matrix R of A;');
+T = A;                   //Temporary matrix to store A
+//R1 = R1 - R4 and R2 = R2 + R4
+A(1,:) = A(1,:) - A(4,:);
+A(2,:) = A(2,:) + A(4,:);
+//R2 = R2/2
+A(2,:) = 1/2 * A(2,:);
+//R3 = R3 + R2 and R4 = R4 - R1
+A(3,:) = A(3,:) + A(2,:);
+A(4,:) = A(4,:) - A(1,:);
+//R3 = R3 - R4
+A(3,:) = A(3,:) - A(4,:);
+//R3 = R3/3
+A(3,:) = 1/3 * A(3,:);
+//R2 = R2 - R3
+A(2,:) = A(2,:) - A(3,:);
+//R2 = R2/2 and R4 = R4 - R2 - R3
+A(2,:) = 1/2 * A(2,:);
+A(4,:) = A(4,:) - A(2,:) - A(3,:);
+//R1 = R1 - R2 + R3
+A(1,:) = A(1,:) - A(2,:) + A(3,:);
+R = A;
+A = T;
+disp(R,'R = ');
+disp('Then we obtain all the linear functionals f by assigning arbitrary values to c2 and c4');
+disp('Let c2 = a, c4 = b then c1 = a+b, c3 = -2b, c5 = 0.');
+disp('So, W0 consists all linear functionals f of the form');
+disp('f(x1,x2,x3,x4,x5) = (a+b)x1 + ax2 -2bx3 + bx4');
+disp('Dimension of W0 = 2 and basis {f1,f2} can be found by first taking a = 1, b = 0. Then a = 0,b = 1');
+//end