3 3 17) Let T be a linear transformation from R° to R, andu and v be orthogonal vectors. Which of the following pairs of vectors must be orthogonal? a) Tu and u b) Tv and v Tu and Tv c) d) ru and sv (where r and s are real numbers) e) u+v and u-v

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

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Q: If three vectors vị, v2, V3 E R° are linearly dependent, then one of them must be a scalar multiple…

A: GIVEN THREE VECTORS v1, v2, v3 belongs to R^3 are linearly dependent

Q: 6. Let a = (1, 0,3) and u = (2,-1,5). a.) (5 pts.) Evaluate projau. b.) (5 pts.) Find a vector that…

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Q: If able please provide a visual representation , this question is from linear algebra: Let P and Q…

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Q: Given vector v = (-6, 4), find -0.5v graphically by stretching the vector by its tip and then…

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Q: Suppose V₁ = vector 1= Write five different vectors in Span{V₁, V2}. For each vector, show the…

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Q: Sketch 2v, -w, v+w, and 2v-w for the vectors in Figure 24. 5 y 4 3 v = (2,3) 2 1 w = (4, 1)

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Q: Let T: R2 R be a reflection in the x-axis. Find the image of each vector. (a) (7, 6) (b) (9,-3) (c)…

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Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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Q: {0·0·0} - {0·8·0} - {0···0} II. I only B II only CI and II only DI and III only

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Q: Consider the vectors u₁ = ------- 2 and the vector : 3 B = If IS in the span of ₁, ₂, 3, 4, write…

A: The given vectors, and the vector .The aim is to find the coefficient of the linear combination of…

Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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Q: Find the direction vector in the same direction of the subtraction vector of theses vectors A = 4ax…

A: We have to find the direction vector in the same direction as the subtraction vector of the vectors…

Q: B) Use vectors to check whether the points A (1,-1,0), B (2,1,-1), and C (-1,1,2), are vertices of a…

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Q: Let u = (2, −1, −1) and v = (5, -3, 3). A vector with integer components perpendicular to ū and v is…

A: <-6, -11, -1>Explanation:Step 1: Determine how to find the perpendicular vector To find a…

Q: Give the vector equation of the plane passing through P, Q, and R. P = (8, 8, 8), Q = (4, 0, 2), R =…

A: The answer is given below:

Q: a) Write an algebraic rule that would translate a figure 15 units right and 13 units down. (x, y) →…

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Q: (a) 3u7 u3 (b) (c) u2 (-2u5) (d) 2u2 : (-u5)

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Q: #1: a) Express v = (2,13,6) in R³ as a linear combination of the following vectors vị = (1, 5, – 1),…

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Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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Q: Let a = (2, 2, -1) and u = (0, 5, 3). Evaluate projau. a.) b.) Find a nonzero vector that is…

A: Let a = (2, 2, - 1) and u = (0, 5, 3)a.) Evaluate proj_a(u)b.) Find a nonzero vector that is…

Q: Consider and remember that A = (0,4,2) , B = (6,-1,0), C = (3,0,1) 1 1) Determine the unit vector…

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Q: Sketch a graph of each vector. 1) a = (9, -12)

A: According to our terms and conditions I have solved first part for next question repost

Q: Q3 O Let w-l(a,b,c), b= 3a} is Sub Sehoof RE a Sub Spaceef R32 is s w X, = i +2j - K , Xz= -3i+2j-R…

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Q: B) ty A' Draw the vector v from a vertex of AABC to its image in AA'B'C'. 8' Determine the…

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Q: 3) Check whether the vectors V, =[1 3 3 5.V =[3 10 6 7]'.v, = [2 7 3 2] e linearly are independent.

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Q: Let a, b, and c be vectors. Is it a vector, scalar, or is in meaningless? 1) ( a X b ) + a.b 2) -2 +…

A: We will whether the part 1, 2 and 3 are a vector or a scalar or meaningless as following.