SOLUTION: show whether the following vectors are dependent or independent u1(1.1.2.2) u2(1.2.3.2) u3(-1.1.2.1) u4(2.2.2.1)

Algebra ->  Linear-equations -> SOLUTION: show whether the following vectors are dependent or independent u1(1.1.2.2) u2(1.2.3.2) u3(-1.1.2.1) u4(2.2.2.1)      Log On


   

Question 698554: show whether the following vectors are dependent or independent u1(1.1.2.2) u2(1.2.3.2) u3(-1.1.2.1) u4(2.2.2.1)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

u1(1,1,2,2) u2(1,2,3,2) u3(-1,1,2,1) u4(2,2,2,1)
We form the matrix %28matrix%284%2C1%2Cu%5B1%5D%2Cu%5B2%5D%2Cu%5B3%5D%2Cu%5B4%5D%29%29 =
We reduce the matrix to row-echelon form
R2-R1->R2

R1+R3->R3

-2·R1+T4->R4

-2R2+R3->R3

R3+R4->R4

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