MATH 2331 Lecture : Introduction to Linear Algebra
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January 31, 2014 x + 2y + 3z = 39 x + 3y + 2z = 34. These three equations represent a plane in r3; we are looking for the intersection of the planes. To nd the solutions, add and subtract multiples of equations. x + 2y + 3z = 39 x + 3y + 2z = 34 ( i) 3x + 2y + z = 26 ( 3i) x + 2y + 3z = 39 ( 2ii) 4y 8z = 91 (+4ii) y z = 5 x + 5z = 49 y z = 5. 12z = 111 ( 12) x + 5z = 49 ( 5iii) y z = 5 (+iii) z = 37.