= L Consider the space P2 which is the vector space of polynomials of degree not greater than two. We define the inner product in P2 according to the formula Also, consider the following two vectors (a) Calculate the inner product (p, q) (b) Calculate the distance between vectors p and q. (c) Calculate the norm ||ql|, of vector q. (p, q) = pqdz. p=r² - 5x+1, q = -2x² + x.

Q: Determine nonzero vectors that are orthogonal to the following vectors. (a) (1, 5)     (b) (6, −1)…

A:

Q: Let v = [2 10. (a) How many vectors does Span {v} contain? (b) List a few vectors in Span {v} and…

A:

Q: Find the cross products u xv and vxu for the vectors u = = (3,5,0) and v = (0,3, - 6). uxv = (Di+…

A:

Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

A:

Q: Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 15.- Find the…

A: Introduction: Vector Operations are operations that are performed on vector quantities. Vector…

Q: ? (2,3), (0,0) }

A: Let S=2, 3, 0, 0. We need to find whether the set S spans a line or all of ℝ2.

Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

Q: Let u be a vector of length 3 in the direction of the positive y-axis and let v be a vector of…

A: Vector: - The term vector comes from the Latin word vector, which means "carrier." Vectors transport…

Q: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

A:

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

A:

Q: Let V₁, V2, V3 be the vectors in R³ defined by 18 ---A V2 = -14 (a) Is (V1, V₂, V3} linearly…

A: We now solve this questions