QUESTION 4 The cross product of u = (6, 7, -8) and v = (7, -5, -9) is given by O (42, –35, 72) 79 O (-79, – 103, –-2) O (9, 94, -103) O (-103, -2, -79) O (-94, 103, -9) O -79 O (103, 2, 79) O None of the other options.

Q: Question 3 Let the basis B = {v=(1.2.3), u=(2, 1, 2), w= (3.-3, 1)} andx=(3, 2,-1). 1. Write the…

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Q: Question 4: Let T be defined as T (v1, v2, v3) = (v1-v2+v3, v2-v3, vl+v2) a) Find the image of (1,…

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Q: The points A(1, 0, 2), B(2, 0, 1) and C(1, 2, k) from a triangle of area √6. Determine the value(s)…

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Q: 1 - 3 2 Let v, = - 3 -2 Determine if the set {v4 is linearly independent. 7 -2 - 4

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Q: 2. A triangle has vertices at (-2, 3), (3, 4) and (4, -1). If this triangle is dilated by a factor…

A: Explanation and solutions is given below....

Q: Question 12 Let = --0---0--0 (:). = -4 -2 10 in R3. Determine whether the given vectors span R³. =…

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Q: Question 4: Let T be defined as T (v1, v2, v3) = (vl1-v2+v3, v2-v3, v1+v2) a) Find the image of (1,…

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Q: Question 4: Let T be defined as T (v1, v2, v3) = (vl1-v2+v3, v2-v3, v1+v2) a) Find the image of (1,…

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Q: 2. Given A = {1,2,3}, B = {7,apple, .5} and C = {r|x < 3 and r 2 -1}, compute the following %3D %3D…

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Q: 10) (Section 9.7) Use vectors to find the largest interior angle of the triangle with the (1, 2),…

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Q: QUESTION 1: Given the point A(-3, -2) and B(6, 1), find the coordinates of the point P on directed…

A: The solution is:

Q: (-3, 4) (3, 4) (-5, 2) (-2, 2) 2 2) (S, 2) (-5, 0) 6543-2-10 (5,0)x 2345 6 (-3,-2) -1 (3.-2) (-2,…

A: Solution: The objective is to find the translation rule for the given graph

Q: 10) (Section 9.7) Use vectors to find the largest interior angle of the triangle with the (1,2),…

A: Coordinate Geometry Question

Q: Problem V The map X(u, v) = (ucos(v), usin(v), v), (u, v) € R² is a) Regular for any (u, v) E R². b)…

A: It is given that, the map Xu, v = ucos v, usin v, v for  u, v ∈ ℝ2 Then,  the map X is ; a) Regular…

Q: Let u=(1, 0, -2) and v=(2, -1, 0). Find the components of 3(u-2v).

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Q: (1, 2, –1) and v = (6,4, 2) in Rº. %3D a) Show that w = (9, 2,7) is a linear combination of u and v…

A: Here, the given vectors are u=(1,2,-1) &amp; v=(6,4,2) in ℝ3.

Q: Question 5 The coordinates of the vector = (2,15, – 7) in the basis B= (1v=(2,0,1),u=(0,- 3,2),w…

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Q: QUESTION 1 Find the domain of gof, if f(x) =x² and g(x) = Vx-6. %3D O a. x2 6 Ob.(- o, -V6]U 6, 0)…

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Q: If ū = (1,–2, k) is a linear combination from v = (3,0, -2) and w %3D (2, –1, –5),then k = 8. O T O…

A: The solution is given as

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: 3 1 If a = 3 b = C = Draw vector diagrams to represent the following: c a+d f -c+b+d a a+b b d-a d…

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Q: Let u = , v = , and w = .   Find u + v - 3w

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Q: 7. Let u = (-4, 2, 3), v = (5,0, –7), and w (7,-2, –5). Find the components of (a) -u + (v – 3w) (b)…

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Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: Question 11 --0--0--0 -4 -2 10 in R3. Determine whether the given vectors span R³. = Let -5 25 = -8

A: Check whether the vectors are linearly dependent or not

Q: 1. Let a = (1, 1, –1) and b = (2,4, 6). Find the cross product a x b and verify that it orthogonal…

A: Given: a=1, 1, -1b=2, 4, 6 To Find:  To find the cross product a×b, and, to verify that it is…

Q: 6) a translation maps A(5,1) to A'(8, 2), what will be the coordinates of B, the image of B(-2, 3…

A: Given a translation maps A(5,1) to A'(8,-2). To find the coordinates of B', the image of B(-2, 3)…

Q: Question (2) 으 (2-3)" P(군)= Let then : %3D a Determine Zo=? and ana? b) Determine the Covergance…

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Q: 10. Let ā = (1,2) and b= (2,1). Find projz(ā). Then show that ā– projz(ā) is orthogonal to b…

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Q: Question 4: [2 Mark] Determine whether or not the given vectors in R" form a basis for R": a) v₁ =…

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Q: If H = {A; A = {i, 2i ,3i, ...}, i E Z} then N-3 An %3D %3D O (-6,-12,-18,..) O {-4,-8,-12,.} O…

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Q: 4. Find the value(s) of a for which and are orthogonal: a) (2,-4,5) and (a +1,3,-a +3) b) -…

A: As per guidelines we must answer only one of multiple questions given. Please resubmit the remaining…

Q: In Exercises 1–8, find the length and direction (when defined) of u * v and v * u.

A: The vectors are: u = 2i - 2j - k v = i - k Then we get,

Q: Let u=(4,-2) ,v=(-2,2) Find component from 3u

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Q: 2. A triangle has vertices at (-2, 3), (3, 4) and (4, -1). If this triangle is dilated by a factor…

A: Given, A triangle has vertices A-2,3,B3,4, and C4,-1. If the triangle is dilated by a factor 2. Then…

Q: The vectors 4 -2 -2 2 12 -5+ k 4 are linearly independent if and only if k +

A: A set of n vectors is  linearly independent vectors if the matrix with these vectors as columns has…

Q: 5. B1 = {(1,0), (–1,1)} and B2 = {(1,2), (-1,0)} are two bases of IR?. Let u = (2, 1) and v = (4,…

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Q: Question Six: (. Let = (1,-1,0,4) and = (1,-1,2,0). Find a vector WE R4 that satisfies 4u wü.v(u - 2…

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Q: Example 19-1. Given Uo = 3, U1 = 12, U2 = 81, U3 = 200, U4 = 100 and U = 8, find %3D %3D %3D %3D

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Q: 26. Areas A, B, C, and D as shown in the figure below are rotated counterclockwise by 75° with the…

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Q: QUESTION 12 Given two sets A = {1,2,3} and B = (a,b,c} Let AxB be the cartesian product of A and B.…

A: The two sets are defined as follows: A=1, 2, 3 and B=a, b, c Definition: The cartesian product A×B…

Q: 1 a)Let a = (1, 2, 3) and b = (−1, 3, 2) Compute 5a + 7b. b)Compute the angle between (1, 2, 1)…

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Q: Question. 2 Show that Span (x₁,x2,...,x,y) = Span (x₁,x2,...,xn) if and only if y is a linear…

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Q: Question 1: Determine whether each vector can be written as a linear combination of the vectors in…

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Q: 12. Which of the following is the vector equation of a plane that contains the line 3+2-¹ and the…

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Q: Plot the points on the same three-dimensional coordinate system. (a) (2, 3, 1) (b) (-1, 4, 2) 8. z -…

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Q: Question 3 of 5 (1 point) Question Attempt: 1 of 1 Time Remaining 1 = 4 Find the area and perimeter…

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Q: Let u = (-3, 1, 7), v = (3,0, -6), and w = (6, -1, –3) Find the components of v – w. (-4, 1, 3) V -…

A: Given u = (- 3, 1, 7), v = (3, 0, - 6) , and w = (6, - 1, - 3) Find the components of v — w.