Let V₁ = a) [¹ b) c). [3].2012 be 2 vectors in R². Show that S = {v₁, v2} is linearly independent. Find a basis for R². v2 = | Let v = [7³] ER². Write v in terms of v₁, v2.

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

A:

Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

Q: Find each of the following Given: u = ; v = ; w = 1. u.v 2. (u.v)w 3. u.(2v)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: To express the vector =(1.2 -6) as a linear combination of three vectors ,- (0.1. 2), v= (1,0.2) and…

A:

Q: Find each vector sum u + v. a. u = (1, 4), v = (2, −2) b. u = (3, −2), v = (−3, 2) c. u = (2, 1), v…

A: a). b).

Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

A:

Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

A:

Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

Q: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

A:

Q: Let v = (7,8). Suppose w E R2 is perpendicular to v, and that ||w|| = 9. Find both possible vectors…

A:

Q: If possible express the vector v as a linear combination of V1, V2, and V3.

A:

Q: Let v= (4,5,8) and w=(-10,-8,9) be vectors. Find the scalar component of v in the direction of w.…

A: For vectors v , w , the scalar component of v in the direction of w is given by Sw(v) = v·ww And for…