Question 698554

u1(1,1,2,2)  u2(1,2,3,2)   u3(-1,1,2,1)  u4(2,2,2,1)

We form the matrix {{{(matrix(4,1,u[1],u[2],u[3],u[4]))}}} = {{{(matrix(4,4,

1,1,2,2,
1,2,3,2,
-1,1,2,1,
2,2,2,1))}}}

We reduce the matrix to row-echelon form

R2-R1->R2

{{{(matrix(4,4,1,1,2,2,
0,1,1,0,
-1,1,2,1,
2,2,2,1))}}}

R1+R3->R3

{{{(matrix(4,4,1,1,2,2,
0,1,1,0,
0,2,4,3,
2,2,2,1))}}}

-2·R1+T4->R4

{{{(matrix(4,4,
1,1,2,2,
0,1,1,0,
0,2,4,3,
0,0,-2,-3))}}}

-2R2+R3->R3

{{{(matrix(4,4,
1,1,2,2,
0,1,1,0,
0,0,2,3,
0,0,-2,-3))}}}

R3+R4->R4

{{{(matrix(4,4,
1,1,2,2,
0,1,1,0,
0,0,2,3,
0,0,0,0))}}}

The all-zero row at the bottom tells us the
matrix has rank 3 and nullity 1, thus those 4 
vectors are dependent.

Edwin<pre>