Given that 7 write 3 5 7 3 5 -2 2 3 7 -1 2 2 3 3 125 100 010 -5 001 3 as a linear combination of the vectors 2 332 2

please show all your work vectors

If Fins ā -b and %3D SICETCH THE ComputAtiON 1iBOVE A VECTOR ADDITION AND REPRESENT IT AS

Let u1, U2, ..., un be a set of vectors, and suppose there are nontrivial solutions to x11x2u2+ +xnun = 0 Explain why, if x is a free variable, you can always express u; in terms of the vectors corresponding to the basic variables.

The following question is from linear algebra first year: Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step. Can we get integers as answers?

Given that -0 4 write 1 || = 0 1 0 -1 0 -1 -1 0 1 4 as a linear combination of the vectors 1 ~ 0 0 1 0 0 2 1 0 0 1 1 N N 0 -2 16. " +

. Create a vector named prob18a that has 10 elements of which the first is 8, the increment is 7, and the last element is 71. Then, assign elements of prob18a to a new vector prob18b such that prob18b has 7 elements. The first 4 elements of prob18b are the first 4 elements of the vector prob18a and the last 3 elements of prob18b are the last 3 elements of prob18a. Do not type the vector elements explicitly.