Let V be the plane with equation ₁ + 3x2 − 4x3 = 0 in R³. Find the matrix A of the orthogonal -14] projection onto the line spanned by the vector 2 {10} -2 A= = = with respect to the basis

Q: Find the sum of the vectors (–1,4) and (6, –2) and illustrate geometrically.

A: A vector V→=a,b can be represented on the cartesian plane, From the vector law of addition,…

Q: Let (3,-1,2) and (1,4,-1) be co-planar vectors(two vectors that sit in the same plane). Find a…

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Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

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Q: i) Using Gaussian Elimination method, verify that x, = 2, x2 = -1, and x3 = 3. ii) Show that b is in…

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Find the projection of the vector a = (2, 5, 1) on the vector b = (1, 1, 3) O a. (10/11)(ax + 3ay +…

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: Find an orthonormal basis of the plane x₁ + 3x2 − x3 = 0.

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Q: Calculate the scalar products of the following vectors: 10 1 Q-B 5 W1 -4 9 (a) V₁ = (b) V2 = (c) V3…

A: Note: As per rule I need to solve only first three subparts.

Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: Find the change-of-coordinate matrix P from B to C and P from C to B for the bases B = {1,t,t^2} and…

A: Let U={u1,u2,⋯,un} and V={v1,v2,⋯,vn} are two bases of a vector space W.The identity map I:W→W…

Q: Express the vector p = (-6,15,-3) as linear combination of the vectors u = (1,-1,3), v = (2,-5,0)…

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Q: Let V be the plane with equation x-2x - 4x = 0 in R. Find the matrix A of the orthogonal projection…

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Q: The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

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Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: 3) Find the vector projection of A onto B. (Projs A). b\ If possible, use matrix inversion method to…

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Q: Show that the column vectors (1,1,2,4),(2,-1,-5.2) (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Find a complex vector d so that if F{(fo, ƒ1, ƒ2 ƒ3)} = ċ then F{(−fo, − ƒ₁, 0, 0)} = č ® ā.

A: According to the given data, find the vector d:

Q: Vektor m =[5, -2, 1] Vektor n =[-6,-2, 4] a. find vektor p where p = -2m+0.5n b. find vektor…

A: a) write p in terms of m and n with the given relation p =…

Q: Verify the identity Ax(BXC) = B(AC) - C(A-B) using the following vectors A = ax + 2ay + 3az B = ax…

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Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)

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

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Q: Are the vectors ū = [4 -5 4], v = [2 2 -3] and w = [-1 -5 2] linearly independent? Choose If they…

A: To find Whether the given vectors are limearly independent or not.

Q: Find a subset of the vectors that forms a basis of their span: (i) vi = (-1,1, -2,1), v2 = (2,-2,…

A: For (i), Notice that v2=2, -2, 4, -2=-2-1, 1, -2, 1=-2v1. So, the subset of the vectors that form a…

Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

A: We have to prove that the given Column vectors are linearly dependent in R4.

Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: O Find a vector perpendicular to both i- 3j+2k and 5i-j-4k

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Q: Find the coordinate vector (v)s relative to the basis S= {v ,,v,,v;} 21 for v = (2, 1, -2), if V=…

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