Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Form a matrix A from the 3 given vectors in the space of W.

W perpendicular is orthogonal to W, means every vector in that space is orthogonal to every vector in W.

This is possible when A X = O

Find row reduced Echelon form of A :

======================== Dimension of W = rank of A = number of independent rows in A = 2

Null space is the orthogonal space (orthogonal complement) of A, It has [ 1, 2, 4 ]. Its dimension = 1 ( = n - dimension of W)

The operations performed on 1st row to become O are : 7 row1 - 4 Row2 + 2 Row3 = 7 * [2, 0, 4 ] - 4 * [ -1, 2, 0 ] + 2 [ 3, 1, 7 ]

========================

W is a plane in in three dimensional space. x = 2 y = - 2 z (it passes through origin)

W perpendicular is the Line perpendicular to the plane of W.