Is 1 0 2 4 Span0 0 1 01 1 2 10 1 1 1 Answer yes or no and ju

Is (1, 0, 2, 4) Span((0, 0, 1, 0),(1, 1, 2, 1),(0, 1, 1, 1))? Answer yes or no and justify your answer

Solution

Run this matlab code:

clc
clear
A2= [0 0 1 0 ; 1 1 -2 1; 0 1 1 1]
B2=[ 0 0 1 0 ; 1 1 -2 1; 0 1 1 1; 1 0 2 -4]
r1= rref(A2)
r2= rref(B2)
r3= rank(A2)
r4= rank(B2)

Answer

A2 =

0 0 1 0
1 1 -2 1
0 1 1 1

B2 =

0 0 1 0
1 1 -2 1
0 1 1 1
1 0 2 -4

r1 =

1 0 0 0
0 1 0 1
0 0 1 0

r2 =

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

r3 =

3

r4 =

4

>>

>> Since rank of r3 and r4 is 3 and 4 and they are not equal ,Hence answer is \'NO\' thus justified