- X3 + 5x4 = 0 X2 + 4x3 – 3x4 = 0 X1

Let -0-0-0-0 V2 = w= -5 = -2 = = If possible, express w as a linear combination of the vectors V₁, V2 and v3. Otherwise, enter DNE. For example, the answer w = 4v₁ + 5v2 + 603 would be entered 4v1 + 5v2 + 6v3.

Express the vector v =-1 as a linear combination of the vectors --3 V1 0,v2 4 and v3 -4 , if possible. Show all of the steps that you used %3D 3 -2 11 in obtaining your solution. 3.

The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v- If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6)

Write the vector as a linear combination.   PQ where P=(3,6) Q=(1,-3)

Calculate the linear combination: 1 (2, 2, –4) + 4 (–2, 3, 2) =

Illustrate with an example and a diagram why a+b=6+a¯ for all vectors a and b

if given the equation yi = B0 + B1xi +ui and express the same equation as y = xiB = ui (where xi and B here are vectors), does vector xi = [1 x1] or xi = [x1] (row vector) and B vector (column vector) = [B0; B1]?

Express each column vector of AA as a linear combination of the ordered column vectors C₁, C2, and c3 of A. -6 A = 6 2 4 3 Enter first column as a linear combination of columns of A in terms of the vectors C₁, C₂, and c3: Enter second column as a linear combination of columns of A in terms of the vectors C₁, C2, and c3: Enter third column as a linear combination of columns of A in terms of the vectors C₁, C₂, and c3:

Assume v1 = [3,-2] and v2 = [-1,4].  Find the sum and difference of vectors v1 and v2. v1 + v2 = [Answer,Answer] v1 − v2 = [Answer,Answer]