4. Which point is coplanar with E, F, and H in the diagram below? В O c О в O A O G A Н E D G с F

Q: 1.5 Let u = (-1,0,1) and v= (2,-1,5). 1.5.1 Writev in component form and determine [v]. 1.5.2…

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Q: Which of the following graphs shows interaction between x1 and x2 in their effects on y? a) b) B. a…

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Q: (x + y + z) dA. 3,

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Q: 25. Show that |v|u + Ju|v and |v|u – |u| v are orthogonal.

A: Two vectors are orthogonal if their dot product is zero. If the dot product of two vectors is zero,…

Q: 4. For what value of h is vz in Span {v, v2} and for what value of h is {v1, V2, V3} linearly…

A: v1=1-32, v2=-39-6 and v3=5-7h

Q: 21 - Let V = R3,S = 5 Show that = Span(S) %3D

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Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: Q.2: Find u x v, where a: u = (1,–3,4) & v = (3,4, 7), ats b: и %3D (1,2,3) &v %3D (1,5, 2).

A: Given: a u=1, -3, 4 and v=3, 4, 7b u=1, 2, 3 and v=1, 5, 2 To Find: u×v=?

Q: 39. The vertices A, B, C of a triangle have position vectors a, b, c respectively. The area of this…

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Q: 1. Letz =1+i,1,=-1+i, locate the numbers z+ z, and , vectorially in the rectangular coordinate…

A: We are Given that : z1=1+iz2=-1+i ⇒z1+z2=(1+i)+(-1+i)=2i and  ⇒z1-z2=(1+i)-(-1+i)=1+i+1-i=2

Q: Evaluate Əw at (u,v) = (1,2) for the function w(x,y)=xy-y²; x = u-v, y = uv. ди OA. -1 B. 3 O C. 1…

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Q: -U 1. Let the vector u = -i +3j+k, find 12

A: Solution :

Q: a. Let C = C, U C2 where C, is the line segment from (2,0,0) to (3,4,5) and C2 is the line segment…

A: c1: Line segment from (2,0,0) to (3,4,5)The equation is…

Q: + Let A = B = 1 4 Then find: AB & BA - 2

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Q: 10. Given two vectors u = [2,4] and v = [6,2]. determine the projection of u on v.

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Q: Let u = (-1, 1, 0) and v = (-7, 6, -5).

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Q: Compute F. Oszs V1-x2 –y? Let E be the hemisphere described by and F=Vz2 + x² +y² i + Vz² + x² + y²…

A: By Gauss divergence theorem:∬∂EF·nds=∭Ediv(F)dvhere givenF=x2+y2+z2( i^+j^ +k^…

Q: Which of the following maps from R² to R³ are R-linear? 2 f(x, y) = (x. x - 2. x+y+z) f(x, y) = (x…

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Q: 13. 2 [3] and u = [4] vectors, one in Span {u} and one orthogonal to u. Let y = . Write y as the sum…

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Q: Compute u X v.

A: Here given vector as u=3-12, v=011 These vectors can be written as u=3i-j+2kv=j+k

Q: 5. For which value of x do the following vectors form a linearly dependent set in R -1 y =|x, in- х,

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Q: Assume m₁ = [4., 1.5] and m₂ = [1.5, 0.5] represent the mean vectors of pattern class 1 and class 2,…

A: To find the decision boundary between two classes, we need to find the equation of the line that…

Q: -2 B-BL and u= 6 -1 Compute the distance d from y to the line through u and the origin. Let y d= = =…

A: y and u are two points.d is the distance between the point y and the line passing through the point…

Q: 2. Which of the following lines in standard form is equivalent to y OA. 2x+y=1 OB. x + 2y = 1 Oc.…

A: We have given that y = 2x + 1

Q: 98

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Q: J₁ R - x + 3y = 0, x + 3y Round your answer to 4 decimal places. Find - x + 3y -dA, where R is the…

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Q: Which of the following sets of vectors are linearly independent? (Check the boxes for linearly…

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Q: Find the pro ection of v on the line with equation

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Q: S. Re{z²}dz; C is the square with corners 0, 1,1+i, i. [1+i]

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Q: Consider the Simple Linear Model: 4 = Bo + Biz, + e, where i = 1,...,n, and e ~ IID(0, o?). Suppose…

A: Simple linear regression model: A simple linear regression model is given as y = b0 + bx, where y is…

Q: Consider the following. 3D(6,-1,0) v = (-2, 3, 0) u = %3D Find u x v. Determine if uxvis orthogonal…

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Q: 1. 0, dij ss, Otherwise. Tij

A: The given parameter is: