[0 (a) Determine the orthogonal complement of W. (b) What is the projection of y onto W? (c) Write y as a sum of a vector in W and the other vector in the orthogonal complement of W. 3. Let B= and W = span B.

Q: (a) A: va+v. (b) A: (av). (c) A: √ av.

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

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A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: Consider the points A(1,2, –1), B(2, – 1,3) and C(-2, 0, 1) in R³. Define V = 2AB – BC (a) Find the…

A: (a) Calculate the vectors AB and BC and thus find the vector V. A1,2,−1, B2,1,3 and…

Q: Determine the vector fald of . Fa, -- %23

A: The given vector field is                                            V(x,y)=4i-2j

Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

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Q: The vector projection of u = [3, -4, -2] on the x-axis is: %3D 3 29 3 29 3í

A: The direction ratios of the X-axis are, (1,0,0) Also, u•(1,0,0) = 3 is the scalar projection on the…

Q: I'm still confused on the position vector. The question is Let r(t) be the position vector…

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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: Make all obvious simplifications.

A: We have to solve

Q: 3. 4. If =(-12, 4, 8) the position vector of u is.............

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Q: -{{} O Consider the bases B = Find the B-coordinate vector of i= (2, –1).

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Q: Which of the following statements is not true for vectors a, b and c and scalars a and B (A) a.b+a.c…

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