1. The problem statement, all variables and given/known data Complete the square using the symmetric matrix that defines the given quadratic form: ##x^2 - 4xy + 6xz + 2xt + 4y^2 + 2yz + 4yt + 5z^2 - 6zt - t^2## and write this quadratic as the sum and difference of squares after completing the square using the matrix. 3. The attempt at a solution So first I found the 4x4 matrix, using x as the first column, y as the 2nd, z as the 3rd, and t as the 4th. Also x is 1st order, y is 2nd order, z is 3rd, and t is 4th: http://i2.minus.com/inT7VWSkOu3GH.png [Broken] If I want this in reduced row form, I have to switch some rows, name the 2nd and 3rd rows. What implications will this have on my work in completing the square? Also, I couldn't find anything online about how to complete the square using matrices.