Question

Linear Algebra

10. [10 points] Consider the plane P represented by the equation 2z+3y-2z = 0. (a) Find a basis for P. (b) Find a basis for the intersection of P with yz-plane

Answer 1

"The plane 2x + 3y - 2z = 0 is the Null space of the matrix A = [2 0 0 3 0 0 -2 0 0]. [Because Null space of an m times n matrix A, written as N_0/A, is the set of all solutions to homogeneous eq^m A_x = 0] Basis of plane 2x + 3y - 2z = 0 will be Basis of Null space of matrix A = [2 0 0 3 0 0 -2 0 0] To find Null space of A, we find general sol^n of A_x = 0 [2 0 0 3 0 0 -2 0 0] [x y z] = [0 0 0] = > 2x + 3y - 2z = 0 Since it is a homogeneous system of eq^n s