CIVE115 Study Guide - Final Guide: Four-Dimensional Space, Parallelepiped, Triple Product

• School: University of Waterloo
• Department: Civil Engineering
• Course: CIVE115
• Professor: David Brush

Document Summary

If it has a dependant row or col then its determinate=0, there is no inverse, and its rref is not the identity matrix: cramer"s rule, another way to solve for a system of equations. Ay, and az respectively: then to find the values of x, y, and z we just divide the determinate of matrix ax, ay, and. Az by the determinate of matrix a: for example for the matrix to the left, matrix a, ax, ay, and az are shown. I will skip over how the determinates are found and list them here: 4: det(a)=9, det(ax)=-5, det(ay)=20, det(az)=-8, therefore the values of x, y, and z are: x=-5/9, y=20/9, z=-8/9. (cid:1873) (cid:1876)(cid:1874) (cid:1875) = (cid:1873) (cid:1874) (cid:1875) sin(cid:4666)(cid:4667)cos(cid:4666)(cid:4667),(cid:1875) (cid:1857)(cid:1870)(cid:1857) (cid:1871) (cid:1872) (cid:1857) (cid:1853)(cid:1866)(cid:1859)(cid:1857) (cid:1854)(cid:1857)(cid:1872)(cid:1875)(cid:1857)(cid:1857)(cid:1866) (cid:1873) (cid:1853)(cid:1866)(cid:1856) (cid:1874) (cid:1875) (cid:1857)(cid:1866) (cid:1872) (cid:1857)(cid:1877) (cid:1853)(cid:1870)(cid:1857) (cid:1868)(cid:1853)(cid:1855)(cid:1857)(cid:1856) (cid:1872)(cid:1853) (cid:1872)(cid:1867) (cid:1872)(cid:1853) (cid:1873) (cid:1876)(cid:1874) (cid:1853)(cid:1866)(cid:1856) (cid:1875) ,(cid:1853)(cid:1866)(cid:1856) (cid:1871) (cid:1853)(cid:1871) (cid:1856)(cid:1857)(cid:1858)(cid:1866)(cid:1857)(cid:1856) (cid:1853)(cid:1854)(cid:1867)(cid:1874)(cid:1857)