Select the correct statements for W = { [₂] € R²|2₁ · 2₂ ≥ 0}. The zero vector is in W If u, v € W, then u + v € W If u € W and a € R, then au € W W is a subspace of R²

Q: Prove the Py the goreen th : ortho gonel vectors product spoce V. Prove Suppose O and v in an inner…

A: we know that ||u+v||2=<u+v,u+v> now,…

Q: Characteristic spaces of a normal operator are pair-wise orthogonal.

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Q: baisis for the subspace of K of Find that consists of all vectors of the forMm Ca, b, c,d) d= a-7b.…

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Q: coplanar.

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Q: Show that if S={v,v2,V3} is linearly independent and v, is not in Span{S}, then {V,V2, V3, V43 IS…

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Q: 0 1 0 0 0 0 Let A = 1 Then null(A) is and im(A) is

A: Ans:-   Let  A=010001000    we have to find Null A   &  im A

Q: Show that the point (, j) lies on the least-squares line determined by the given set of points.

A: To show that the point  lies on the least-squares line determined by the data points  with . where…

Q: TRUE OR FALSE In each case, explain or prove your answer. R2 is a subspace of R3.

A: A subset W of vector space V is said to form a subspace of V if: for u,v∈W, we have u+v∈W u∈W and…

Q: What is the definition of the orthogonal complement of subspace W?

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Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

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Q: Describe geometrically all the subspaces of R³.

A: I will find all subspaces of R, R^2 and finally R^3.

Q: Consider the following. (a) Show that the set of vectors in R" is orthogonal. (v5, V5. V5) · (0, Vz.…

A: A set of vectors is said to be orthogonal if dot product of any two different vectors of the set is…

Q: Current Attempt in Progress Find the scalar triple product u · (v x w). u-(-8,4,4), v- (5,1, - 4), w…

A: Given: u=-8,4,4, v=5,1,-4, w=-7,4,3 To find: u·(v×w)

Q: Linear Algebra Given B = v1 {(0, 1, 1, 1)}, v2 = {2, 1, –1, –1} , v3 {(1,4, –1,2)} , v4{(6,9,4, 2)}…

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Q: 3 then Fdt is If F=(3t^2+4t)i+ (2t-5) j+4t^3 k 42i-j+80k I O 42i + 2j-80k .II O 421-21+80k.I O

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Q: Challenge A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the…

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Q: Use the function to find the image of v and the preimage of w. T(v,, v2) = v, - V2, V1 + V2, 2v, -…

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Q: Linear Algebra  find a representative of x (vector)

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Q: Regression Line: y=mx+b The regression line (least squares line, best-fit line) associated with the…

A: The given data is as follows: Percent recovery (%)Economic Value ($ Billions)1020040900501000802000

Q: 1. Proof the remaining Dot product properties Let a = (1,2, –3), b = (0, 2, 4), and c = (5, –1,3).…

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Q: If W is a subspace of R and v is any vector in R", then ||projwv|+|v-projwv||2= |v||2.

A: Introduction: Every vector that doesn't lie in a subspace can be uniquely expressed as a sum of two…

Q: reflection across the x-axis W

A: Given,

Q: Using Cramer's rule find the x, y and z 2x-y+3z=-3 3x+3y-z=10 -x-y+z=-4

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Q: Linear Algebra  1)Calculate the area of the parallelogram in which three consecutive verticesare…

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Q: + 5x + 3x2, 2 +T x + 3x² , 4 + 6x +

A: Show that the vectors are linearly independent or dependent. 1. 3-x+5x2, 2+5x+3x2, 2+7x-3x2 2.…

Q: Determine if the set of functions {e* , xe* , x²e* }is linearly independent or linearly dependent. O…

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Q: Testing for linear independence or linear dependence A) a1= (4, -5, 2, 6), a2 = (2, -2, 1, 3), a3 =…

A: A) Given that,a1=(4,-5,2,6) , a2=(2,-2,1,3) , a3=(6,-3,3,9) , a4=4,-1,5,6To check the…

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R b)show that R° = F1…

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Q: Quadrilateral HIJKHIJK has vertices H(−1, 3)H(−1, 3), I(2, 3)I(2, 3), J(2,−1)J(2,−1), and…

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Q: 5. For which value of x do the following vectors form a linearly dependent set in R³ m=(x + x=(₁…

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Q: 8) Describe geometrically all subspaces of R" for n 1, 2, 3.

A: We will do this for all three parts; n = 1, 2, and 3 (in as clear handwriting as possible)

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: Chain Rule (Multiple independent variables) Let w(x, y, z) = √² + y² + 2² wherer = -7re', y = -te'…

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