MATH 510a Midterm: MATH 51 USC Midterm1 solutions

• School: USC
• Department: Mathematics
• Course: MATH 510a
• Professor: All

Document Summary

Solutions to math 51 midterm 1 july 6, 2016. 1. (a) (6 points) find an equation (of the form ax + by + cz = d) for the plane p in r3 passing through the points (1, 2, 1), (2, 1, 0), and (0, 0, 1). We rst compute two non-collinear vectors parallel to the plane: A normal vector is found by taking the cross product of any two non-collinear vectors which are parallel to p ; taking the cross product of the above two vectors, we get the following normal vector: The equation for the plane p then is. X n which is equivalent to 2x y + 3z = 3. 0 is not in the plane because 2 0 0 + 3 0 6= 3. Therefore the plane cannot be the null space of a matrix. Page 2 of 8: suppose a is a 4 2 matrix whose column space c(a) admits the following description: