Prelim 2 [Solutions]

# 001 2 the null space is necessarily theorthogonal

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: {(0, 1, 0, 0), (1, 0, −2, 1)}. 001 2 The null space is necessarily theorthogonal complement of the row space. 11 14 −1 1 −1 3 we get the row reduced echelon form (b) Row reducing the matrix 02 0 7 31 35 ￿ ￿ 1 0 1 1/2 . A basis for the null space of our matrix is then {(−1/2, −7/2, 0, 1), (−1, 0, 1, 0)}. 0 1 0 7/2 −1/2 −1 −7/2 0 . Writing these as columns gives us ourt matrix 0 1 1 0 2) (8 points) a) Find the matrix P that projects vectors ￿ ∈ R3 onto the plane x +2y − z = 0. v b) (8 points) Express the vector (−2, −2, 1) as the sum of a ve...
View Full Document

## This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell University (Engineering School).

Ask a homework question - tutors are online