(3) Let L be the line y 2r in the plane. Find a matrix C such hat for every vector H plane, the product C U is equal to the orthogonal projection of H onto the line L. in the

Q: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: Let V be the plane with equation z₁ +222 + 3x3=0 in R³. Find the matrix A of the orthogonal…

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Q: Let V1 = 1 v2 = V3 = and y = 4 Let W = span {V₁, V2, V3}. Find the orthogonal projection of the…

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Q: Consider the points P(2,4,3) and Q (1, –5,2) in 3- space. Find the position vectors rī and rz for P…

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Q: Show that in the vector space R³ the vectors x = (1, 2, -1), y = (3, 1, 1), and z = (5, -5,7) are…

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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: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: Q1. (a). Let V = R and define addition and scalar multiplication by: (a, b) e (c, d) = (a +2c,…

A: See the detailed solution below.

Q: Let L be the line in R³ that consists of all scalar multiples of the vector 2 Find the reflection of…

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Q: 3.2.1 Vector Cross Product Let vectors: A = (1, 0, −3), B = (–2, 5, 1), and C = (3, 1, 1). Part…

A: Since, you have posted a question with sub-parts greater than three. We will provide the solution…

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: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Answer is 10.1

Q: Let T: R2 R³ and u, v E R2 such that T(u) = 1 2 -2 and T(v) = 4 -2 1 Find the image under T of the…

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Q: d a vector orthogonal to both u and v.

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Q: Let V be the plane with equation ₁ + 3x2 + 4x3 = 0 in R³. Find the matrix A of the orthogonal…

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Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

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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: Compute the scalar triple product u ( x w) of the vectors u = (0, 7, 6 (-8,0, -3), and = (3, -8,9).…

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Q: Determine all three dimensional vectors that are orthogonal to v = 5î – 51 – 5k

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Q: 6. Project the vector b = (1, 4, 2) onto the plane S that contains the vectors a₁ = (1, 2, 1) and a2…

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