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: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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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: Find the best-fit quadratic function f(t) = co+ c¡t + czť² to the data points (0, 7), (1, 6), (2,…

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Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: Find the parabola y = ax2 + bx + c that best fits the four points (0,0),(1,2),(2,3),(-1,1) by the…

A: Step 1:Step 2:  Step 3: Step 4:

Q: Use the function to find the image of v and the preimage of w. T(v1, v2, v3) = (4v2 - v1, 4v1 +…

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Q: Use partial derivatives to obtain the formula for the best least-squares fit to the data points.…

A: Solution

Q: Find all values a for which the set {(a — 5, 13, 0), (−1, a – 9,0), (4, 0, a — 2)} is linearly…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 +…

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Q: Consider a linear model to explain monthly beer consumption: beer = Bo + Biinc + Bzprice + Bzeduc +…

A: Here, E(u| inc, price, educ, female) =0 and V(u| inc, price, educ, female) =σ2inc2. Here, the term…

Q: Using least squares regression criteria, find the line (form y = ax +b) that would be the best fit…

A: X Y XY X2 Y2   1 2 2 1 4   3 4 12 9 16   5 7 35 25 49 sum 9 13 49 35 69     X¯ =1n Σ Xi…

Q: Bi + B2x that best fits the data points (0, 1), Find the least squares line y = (2,0), (3, 1), (5, –…

A: Given the points 0,1, 2,0, 3,1, 5,-1. Find the least squares line y=β^1+β^2x.

Q: Find the least square approximation of a quadratic function for the following set of data pairs…

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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: A certain experiment produces the data (0, 1),(−1, 2),(1, 0.5),(2, −0.5). Find values for a, b, and…

A: Least square method:  The given equation is y=ax2+bx+c and normal equations are, ∑ y=an+b∑ x+c∑ x2∑x…

Q: Xk Ук Find the least-square line y = a + ax for the data. -4 -1 0 2 3 0 2 -1 3 -2

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4V1 +…

A: Given  T(v1,v2,v3) = (4v2-v1,4v1+5v2)Image of v is given by T(1,-2,-4) = (-9,-6) hence (a). the…

Q: Find the equation y = Bo + B1x of the least squares line that best fits the given data points. (2,…

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Q: Least squares approximation is a method for finding the line with minimum vertical distance from a…

A: Solution is following in explanation step.

Q: Given the data points (-2,-3), (-1, 0), (0, 1), and (2, 7), find the parabola that best fits these…

A: The quadratic equation for a parabola is y=a+bx+cx2 and Its normal equations are given…

Q: (3) Construct a linear spline interpolating (-1, 0), (0, 1), (1, 3).

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 +…

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Q: Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: For the data (-3,9), (-2,6), (0,2), and (1,1) find the line and the parabola that provide the least…

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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: Find the natural spline for the data: x0 = 0, x1 = 1, x2 = 2, and f(x0) = 1.2, f(x1) = 1.3, f(x2) =…

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Q: Use the function to find the image of v and the preimage of w. T(V₁, V2, V3) = (4V2 V₁, 4v₁ + 5v₂),…

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: and .We have to find .