Question

e) From the vector equation in part d, we get this system of linear equations (I changed the variables from ci, c2, and cs to x, y, z so they are easier to use in Geogebra and more familiar): x+3y+z e 0 Originally we solved e 0. Try picking 4 different sets of values for 0 e and using Row Reduction to solve the system of equations. This is good practice. Here is a calculator where you can check your work (just change the last column of the matrix) f) Try to do row reduction more generally, with the variables d, e, f included. What relationship do they have?

Answer 1

Given system of equation is x + 6y + 4Z = 0 x + 3y + z = 0 x + 8y + 6z = 0 implies Ax = 0 where A = [1 1 1 6 3 8 4 1 6] is the co-efficient matrix and x = [x y z] Therefore = [1 1 1 6 3 8 4 1 6] R-2 rightarrowR_2-R_1 rightarrow R_3 rightarrowR_3 - R_1[1 0 0 6 - 3 2 4 - 3 2] r_2rightarrow - 1/3 R_2 rightarrow[1 0 0 6 1 2 4 1 2] R_3rightarrowR_3 - 2R_2[1 0 0 6 1 0 4 1 0] Therefore system becomes x + 6y + 4z = 0 y + z = 0 Let z = c therefore y = -c therefore x = 6c - 4c = 2c where c is any arbitrary constant Hence, the system has infinite number of solution x + 6y + 4z = 0 x + 3y + z