Linear Algebra and Its Applications · Problem 3.1.48

Orthogonality — Gilbert Strang

Mathematics · perpendicular-columns-rows

Problem

The lines

3x+y = b_1

and

6x+2y = b_2

are \_\_\_\_. They are the same line if \_\_\_\_. In that case

(b_1,b_2)

is perpendicular to the vector \_\_\_\_. The nullspace of the matrix is the line

3x+y =

\_\_\_\_. One particular vector in that nullspace is \_\_\_\_.