Upload your study docs or become a

Course Hero member to access this document

**Unformatted text preview: **matrix gives us A-1 : A-1 = -1 1 1-2 1 2 2-1-1 Problem 3 Let ~v = 1 √ 2 1 1 . Note that the plane P defined by x + z = 0 is just the plane normal to ~v . The problem demands a linear transformation T : R 3 → R 3 with kernel ~v and image P . Such a transformation T is given by T ( ~x ) = proj P ~x . To see this, note that ~v , being normal to P , is in the kernel of T . Moreover, T ( R 3 ) = P by definition. So this is the transformation we’re looking for. To find the matrix of T , write proj P ~x = ~x-~x ⊥ = ~x-( ~x · ~v ) ~v. = ( I-proj ~v ) ~x. The matrix of proj ~v is (from HW 3) B = 1 / 2 1 / 2 1 / 2 1 / 2 Thus the matrix of T is I-B , or 1 / 2-1 / 2 1-1 / 2 1 / 2 2...

View
Full Document