Question

let A = [ 1 2 3 4: 5 6 7 8: -1 -2 -3 -4: -5 -6 -7 -8] as a 4x4 matrix

find a basis for the vectorspace NullA

Answer 1

u mean null space?

Answer 2

correct

Answer 3

i used question 8 on this link: http://abacus.bates.edu/~etowne/031811jayawant205examsoln.pdf

as a point of reference, but I'm unsure how to handle two free variables

Answer 4

we reduce the matrix to reduced echelon form

Answer 5

[(1 0 -1 -2 \ 0 1 2 3 \ 0 0 0 -0\0 0 0 0)\] which shows two free variables, and that x(1) = x(3) +2x(4) and x(2) = -2x(3)-3x(4)

Answer 6

there r two non-zero rows, mean that rank=2
since we have rank + nullity =4(order of the matrix)
nullity=2

Answer 7

then does the question even make sense to find the basis for that vectorspace?

Answer 8

u mean the given matrix?

Answer 9

for the null

Answer 10

the link i posted shows how they solved for a 3x3 with one free variable, but im unsure how to proceed with two

Answer 11

oh i didnt check it:)

Answer 12

opabrawl u there?