The set {V1, V2, V3} is independent. Use the Gram-Schmidt process to produce an orthogonal set with the same span. -2 0 0 -1 V1 B = = -1 -1 0 V2 0 0 100 V3 = 1 2 3

Q: 1. If A = find A1000 by diagonalizing. )Show every single step for your work).

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Q: Find the least-squares line y= Bo + B,x that best fits the data (- 4,0), (- 1,0), (0,2), (1,5), and…

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Q: Use Lagrange multipliers to find the point on the plane x-y+z=7 closest to the point (4,5,1).

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Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

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Q: Find the orthogonal trajectories of the family of lines 3x + 5y = C A B C D 3x 5y = k 5x 3y = k 3x +…

A: Orthogonal trajectory

Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

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Q: Find a least-squares best fit line for the points (1, 5), (2, 1), (3, 1), (4, 3). Write your answer…

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Q: Find the plane z = a + bx + cy that best fits the data points (0, -4, 0), (5, 0, 0), (3, -1, 1), (1,…

A: Data points 0,-4 , 0 ,5 , 0 ,0 ,3 , -1 , 1 ,1 , -2 ,1 ,1,-5 , -3. To Find: The plane z=a+bx+cy that…

Q: Find the cross product a * b. a=(4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a and…

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Q: Let ui = (3, –1,3, 3), u2 = (-2,3, 1, 3), and uz = (0, –1, -1, –1). Write v = (8, –9, 1, –1) as a…

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Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

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: 2 Find the best straight-line fit (least squares) to the measurements b=4 at t= -2, b=3 at t = -1,…

A: Let  b=r t+s be the least square straight line fit for given data then we have…

Q: Let V₁ = [], , V3 Determine if the set {V₁, V₂, V3} is linearly independent. ‚ V2 =

A: Definition of linearly independent set

Q: Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

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Q: Find the matrin of linear 2 22

A: The domain of the given transformation is R3:   To find the matrix of the linear transformation,…

Q: Determine if the set is linearly independent. S = {(4,0,1), (0, -3,2), (5,10,0)}

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Q: Show that the set S= {(20, 34), (40, 68)} is linearly independent or not?

A: Given set is S= {(20, 34), (40, 68)}

Q: Find the least squares regression line, using the matrix form for linear regression. (−7, 1), (1,…

A: The linear relationship between two variables x and y can be defined using the equation, y=b+mx. The…

Q: If V1 = [1 4 0] and V2 = [ -2 0 8], then determine all possible 1x3 row vectors V3 such that the set…

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Q: 2) Consider a set of points {(-2,-18), (-1, -7), (0, -2), (1, -3), (2, -10)}. a) The least squares…

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Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: In Exercises 9 and 10, (a) for what values of h is v3 in Span {V₁, V₂), and (b) for what values of h…

A: INTRODUCTION If there is a nontrivial linear combination of the vectors that equals 0, then a set of…

Q: Consider the linear equalion 5x+2y=17. Fis the value of s that makes the given ordered pair (x,1)

A: The given equation of the line and point is: 5x+2y=17 and Px,y=x,1

Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

A: Vertices of triangle ABC are A(2,-3) , B(-2,1) and the centroid of this triangle moves on the line ,…

Q: Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

A: Given. A(x,5), B(2,3) and C(4,-5) are collinear.