Given an orthonormal basis of R³ : {V1, V2, V3} = 1 of the following are the coefficients C₁, C2 and C3? W = C C1 = = 0, C₂ = 1, C3 = −1 C1 = C1 C1 = 13/17,02 = 331,03 = -3/1/20 3√/3 C₂ √2 C3 √3 √2 3 √3 C2 is expressed as a linear combination W = C₁ V₁ + C2 V2 + C3 V3 then which one 3 VZ, Cz 3√/3 √2 1 √3 1 √√3 1 √3 3 √√√72 ₁93 = 3/6 C3 √6 If

Q: Consider the ordered bases B = {(1,2), (–2, 1)} ß = {(1, 2), (– 2, 1)} and B' = {(-7,6), (1, –8)} B'…

A: Given that  β=(1,2),(-2,1) and β'=(-7,6),(1,-8) are two bases for ℝ2.  Also give that…

Q: part (d) and (e)

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Q: Find the cross-product of M x N.  Tip: use the determinant

A: Given M=2(ρsinϕcosϕ+ρcosϕsinϕ)ρ+2(-ρsin2ϕ+ρcos2ϕ)ϕ+zz and N=2ρ2cosϕρ+2ρ2sinϕϕ

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 √(-2¹ - 122³ - 30x²…

A: Since you have uploaded multiple questions, according to our guidelines we have solved first…

Q: 3 Given that u = 4i+ GJ and Iv[ = 2, find vif u and V are or thugonal to each other.

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Q: a' Find the value of a for which S forms a basis for R3.

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Q: 2. Define two ordered bases B = and E = on R³. (i) Find the vector vị of R³ whose component vector…

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Q: Given an orthonormal basis of R³ : {V1, V2, V3} = = 2 [] 7 is expressed as a linear combination u =…

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Q: Vector v has an initial point at (9, 3) and a terminal point at (16, 12). Which of the following…

A: We need to find linear form of vector v.

Q: (e) Explain that Sį is a basis for R3 and that S2 is not. (f) Determine the coordinates of X1 U =…

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Q: Given the ordered basis B = {p1 = 9 + 2æ, p2 = -4 – x}, find [p]B, the coordinates of p = -39 – 9x…

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Q: The set B = {3 + 2x², 6 − 2x + 4x², 4x − 13 – 10x²} is a basis for P₂. Find the coordinates of p(x)…

A: The objective of the question is to find the coordinates of the polynomial p(x) = 18x - 54 - 40x^2…

Q: Consider the two bases B = {b₁,b2} and C = {₁, 2} for R² where 3 5 = = - [B]-4-[13] 4-[8]), 4-[8] =…

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Q: The set B = = {1 − t², t+t², 1 + 2t-t²} is a basis for P₂. Find the coordinate vector of p(t) = 5 +…

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Q: Solve for the value of x, y, and z using Cramer's Rule 8x +15y + 3z = 143 3x - 7y + 13zi = -62 +…

A: We will find out the required solution using Cramer's rule.

Q: The set B={1+t, 2t-t, 1+t+t} is a basis for P₂. Find the coordinate vector of p(t)= -3+7t-7t…

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Q: Consider the following complex matrix: 8 2 M = 3 8 4 8 8 Determine, in terms of a/the variable t,…

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Q: Let Pa represents multiplication by 1+t? with respect to the basis B = {1,t,ť²} for P2 and BU{t,t*}…

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Q: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: Consider the following two ordered bases of R°: {{1,1, – 1), (1, 2, –1), (–1,1,0)}, {(1,1, – 1), (1,…

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Q: Suppose that 0.3210 approximates 0.3245. How many significant digits does the approximate have? O 3…

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Q: Let TilPe ~> Pe, Tlax?+bx+c) = 2QX+ b %3D the basis of NIT) is True False

A: Applying nullity we have

Q: Show that B = {v1, v2, v3} is an orthogonal basis for R3: v1 = (3,−3,0), v2 = (2,2,−1), v3 =…

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Q: Consider the following two ordered bases of R³: B = - {(0, 1, 1), (0,2, −1), (1, −2, 1)}, с = {(2,…

A: a). Change of basis matrix from basis B to basis C.      a11 ​= −1/3​, a21 ​= 1/3​, and a31 ​= −1/3…

Q: Find

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Q: Let TilPe P. Tlax²+ bx+c) = 20x+ b. Then the basis of NIT) is O True O False

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Q: Without using determinants, show that {(2, –x,,3x²,x³} is a basis for Ps then find dimension for P3

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Q: Given the ordered basis -8 6 Α1 - B = = {A₁ A₁ = A2 = -3 7 -7 0 A3 = A4 = -8 -5 -9 2 = [ 6 0 3 [36…

A: Our coordinates of A with respect to B =[2, -1, -3, -2]'' means transpose Explanation:Step 1: Step…

Q: The set B = {2 + 2x², 4 − 3x + 4x², 19 − 9x + 18x²} is a basis for P₂. Find the coordinates of p(x)…

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