If b1,b2 form an orthonormal basis for C² and x is any vector in C², then |x4 — 2 |x · b₁|²|x · b₂|² - O = |x-b₁4 + x.b₂|4 O|x4|x-b₁|- |x-b₂|* O O O = 0 |x|4 — |x · b₁|² = 2 |x · b₁|²|x · b₂|² + |x · b₂|² None of the given options is correct |x|4 + |x · b₁|¹ − 2 |x · b₁|²|x · b₂|² = |x · b₂|ª

Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x*, –1+x…

A: The solution is given as follows :

Q: Let Is S a basis for R³?

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Q: Let B = {1, x, x², x*} be an ordered basis for P3. Find the coordinate vector of f(x) = 4x3 – 72² +…

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Q: The set of all quadratic polynomials P3 is a vector space with standard polynomial operations.…

A: Ww are given a set S={-2x+3 ,-4x+8 , x-2} and <S>, which is a polynomial space spanned by…

Q: Let P3 = {ao+a₁x + a₂x² + 3x³|ao, a₁, 02, 03 € R} be the vector space of polynomials of degrees at…

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Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: The vectors -5 FB-B-B , V2 = 6 -2 form a basis for R³ if and only if k| V1 = 3 -6 0 and V3 = 1 -6 k

A: Given that the vectors v1=3-60 ,  v2=-56-2   and v3=1-6kThe matrix form of the given vectors is…

Q: -6 -2 -2 0 -6 -2 -2. Find a basis for N (A), the null space of A. Let A = [ 0

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Q: { 1 + x + x², x + x², x²}. %3D for P2. Let p(x) = -1 +x + 2x2. Then [p(x)]B = %3D %3D

A: The given basis is B=1+x+x2,x+x2,x2 for p2. let p(x)=-1+x+2x2 We have to find,  p(x)B=?

Q: XI Let W = X2| 0 2X1 -X z+ X4= + Xy = o] be a subset of Rt IRt. which one is the basis for W?

A: Given W=x1x2x3x4:2x1-x2+x4=0 be a subspace of ℝ4

Q: Let B = vector of 7 = E [V]B 0 1 00 {[%] [83] [28] [89]} 9 9 relative to B. -5 -2 || be an ordered…

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Q: 1 1 1 Let A 1 1 1 1 1 1 3/5 -7/5 is in null(A), or 4/5 Either show that the vector show that it is…

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Q: XI Let 2 Xi - X z+ Xq = oY be a %3D Xu subset of IR4. which one is the basis for W?

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Q: Let s= {(1,3.5). (3. 3, 2). (-1, 1.8)} be a basis for R. If u = (8, 8, 1), then (u), - A) (1 2 1 B)…

A: The solution is given as

Q: E Let z = 1+ i and z'=i-1. 1) Are these two complex numbers independant in the real vector space C?

A: We checked two complex numbers independant in the real vector space C?

Q: The coordinates of p(x)=5+3x+x² relative to the basis {1+x,2-x2,3+x+x²} is O (-1,1,2) none (0,1,1) O…

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Q: Iř bị, b2 form an orthonormal basis for C and x is any vector in C?, then O x[4 – 2 |x - b1|² |x -…

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Q: 2 3 [+0 4 2 b = -2 Select true or false for each statement. Let A = and c = [12] 1. The vector c is…

A: The objective of the question is to determine whether the given vectors b and c are in the kernel…

Q: Write the following equations using index notation and Einstein summation convention: (a) (a b)(b c)…

A: The following are the rules in the Einstein's summation convention having the index notation:1) The…

Q: 2 -3" A = 2 –1 4 4 3 -2

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Q: -1/7 -4 /7 4/7 -5/7 U2 = and 4/7 2/7 2/7 4/7 -4 /7 2/7 03 = Find a vector vá in R* such 2/7 -5/7…

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Q: V = [X1 5 1;3 X2 2;4 0 6] A. V(:,2) B. diag(V) C. V(1,1) + V(2,1) + V(2,2) + V(3,2) D. 10: X1 : 40…

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Q: If b1, b2 form an orthonormal basis for C and x is any vector in C, then O x4- x bị x b2 0 O x+ x bị…

A: We will find out the required value.

Q: 7) The vectors. A) True 13 False 17 -19 + -34 38 17 2 form a basis for n

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Q: 5 Find w if (w)s = |0| relative to the basis S = {-3 -5 2 } 2 3 w =

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Q: Which one of the following is an orthonormal basis of R³? {Q.0·0} 1 1 امام امامت امام 0 3 0 L √2 0…

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Q: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

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Q: 4 -3 v1 = V2 %3D form a basis for IR if and only if k

A: Solve the following

Q: -3 Express the general solution of Ax = b where A = and -9 27 b = as x = x, + cxn where x, is the…

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Q: Let v = 3 2. 2. What is the smallest positive

A: Given vectors are: v1=1122 ; v2=1232 ; v3=2134 ; u=321x We have to find the smallest positive…

Q: Let A = -2 -2 5 5 -5 -2 Give a non-zero vector in the null space of A. -5 -2 -1 5 5 1 2

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Q: Af a, B are two vectors in an inner product space V(F) and a, be F then prove that Re (a, B) = || a…

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Q: 2. Consider the basis * B = (1+*+**, x +r, 2). %3D for P2. Let p(x) = -1 + x + 2r?. Then [p(x)]R =…

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Q: Let Pn ={anxn + an-1xn-1 +. . . . + a1x + a0 | each ai is a real number}. Is it possible to have a…

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Q: ow that B = {5+i, 2+i} is a basis for Q(i) whose elements are algebraic tegers. Why is ß not an…

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Q: Which of the following sets form a basis for the vector space P₂(R) = {ax² + bx + c : a, b, c = R}…

A: According to guidelines first three subparts can be solved.