Question

Let v1= (1,1,2,1)
v2= (0,1,3,3)
v3= (1,-1,-4,-5)
v4= (1,0,-2,-4)

a) Let U=span{v1,v2,v3,v4}. Find the dimension of U

b) Is span {v1,v2,v3,v4}=R4?

c) Find a basis for U

Very Much Appreciated!!!

Answer 1

If U=span(v1,v2,v3,v4), then check the rank of the matrix

1 1 2 1
0 1 3 3
1 -1 -4 -5
1 0 -2 -4

(the v's are in rows)

The rank of the matrix is the dimension of U.

This can be done by reducing the matrix to the echelon form. The number of non-zero pivots is the rank of the matrix.

Do you need help with the reduction to the echelon form?