2. Provide detailed justifications for the following questions. a) Consider the vectors: 2 [8] V₁ = V₂ = v=k If it is given that the vector v is a linear combination of the vectors V₁ and V2, then find the unknown k. Provide a detailed solution. Find a vector u that is not in Span{V1, V2}. Justify your answer.

Q: Consider the following vectors: 2 4 3 8 -3 c²= -8 -3 3 7 For each of the following vectors,…

A: Given that              a→=23-33, b→=48-85, c→=2-367

Q: Consider the following vectors: -1 -3 -2 3 -3 4 8 For each of the following vectors, determine…

A:

Q: Consider the following vectors: 3 9 u= = [³₁] · V = [₁0] · W = [-₁0], x= []. V= W= -5 10 X ·

A:

Q: Determine if the vector 2 b -A = 3 5 can be written as a linear combination of the vectors ---- 1…

A:

Q: What value of a will make the vectors (-2, x, 1) and (2, –1, 1) orthogonal? Select one: O a. 3 O b.…

A: For orthogonal, dot product of two vectors are zero.

Q: If u and v are the vectors below, solve the following equation for the vector x. 4 3 u= 4 -1…

A:

Q: Draw a picture of the following vectors, then calculate them algebraically. Make sure you label the…

A: Given: The three vectors:Vector Vector Vector Aim: Draw a picture of the vectors and  on a…

Q: 5. For vectors given the vectors v =(-4,-3) and w (-1,-1), find: (a) Sketch, v+w below. Find its…

A: We can solve as follows

Q: 2. Let vectors a = (3, 1, 2), b = (0, 2, 1), and c = (1, 1, -1) be given. Find (2a + 3b). c. • Find…

A:

Q: Given vectors u = <-3, -7> and v = <-1, 5>, find the resultant vector  u + v.

A: The objective of this question is to find the resultant vector when two given vectors are added…

Q: 1. Write the vector 1 16 as a linear combination of the vectors 1 2 and 2 1

A: Let the given vectors be:w=-7116, u=-112, v=21-5. To Do: We have to write the vector w=-7116 as a…

Q: 4. If possible, express t as a linear combination of u, v, and w. t = (2, 13, 5), = (1,2, 1), v = (-…

A:

Q: Consider the following vectors: 3 9. 1 a= 4 c'= 9. -10 –10 For each of the following vectors,…

A:

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

A:

Q: Let W= W= , V1 = , V2 = V3 = If possible, express w as a linear combination of the vectors v₁1, V2…

A:

Q: draw the vector -u+ 2v + 4w

A:

Q: Express the indicated vector w as a linear combination of the given vectors v₁ and v₂ if this is…

A: Solution:-

Q: 4. Determine if the vectors are orthogonal, in the same direction, or neither. Briefly explain your…

A: