The vectors v1, v2, and v3 are linearly independent. To find the coordinates of the vector v with respect to the basis vectors, we set up a system of equations where the components of v are equal to the dot product of the basis vectors and solve for x, y, and z. The coordinates of v are x=1/4, y=13/4, z=3/8.

1. Show that the vectors v1, v2 and v3 are linearly independent. If the the vector v is in the span
find its coordinates with respect to v1, v2 and v3.
v1 =
4
0
5
2
V2=
0
1
0
0
1
V3=
0
2
2
1
5
V=
1
4
2
4
9
please show work
Solution
4x=1 x=1/4 5x+2z=2 2z=2-5/4 z=3/8 y+2z=4 z=4-3/4 =13/4
v=v1(1/4)+v2(13/4)+v3(3/8)