mooshupork34
Junior Member
- Joined
- Oct 29, 2006
- Messages
- 72
if anyone could show me how to do this lin. algebra problem, i would be grateful!
here it is:
Let x_1,....x_n+1 (that means x sub 1 through x sub n+1...sorry, i dont know how to do subscripts on this thing) be vectors in the set of real numbers.
(a) Show that there exist real numbers a1,....an+1, not all zero, such that the linear combination a_1 x_1 +....+a_n+1 x_n+1 = 0. (Hint: solve an appropriate homogeneous system)
(b) Using part a, show that
x_i = b_1 x_1 +....+b_i-1 x_i-1 +...+b_n+1 x_n+1, for some i, 1 is less than or equal to i, which is less than or equal to n+1, and some b_1,...b_i-1, b_i+1,...b_n+1 is in the set of real numbers.
here it is:
Let x_1,....x_n+1 (that means x sub 1 through x sub n+1...sorry, i dont know how to do subscripts on this thing) be vectors in the set of real numbers.
(a) Show that there exist real numbers a1,....an+1, not all zero, such that the linear combination a_1 x_1 +....+a_n+1 x_n+1 = 0. (Hint: solve an appropriate homogeneous system)
(b) Using part a, show that
x_i = b_1 x_1 +....+b_i-1 x_i-1 +...+b_n+1 x_n+1, for some i, 1 is less than or equal to i, which is less than or equal to n+1, and some b_1,...b_i-1, b_i+1,...b_n+1 is in the set of real numbers.