1. Which of the following is true? a. DIm(M2x2) = 2 b. S = {(1, 2, 4), (-1, -2, –4), (2, 4, 8)} is a Basis of R |1 0 2] c. S = { sa Basis of M2x2 d. None of the above

Q: 1. Determine whether the following vectors form a basis for R. -2 11

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Q: +t, 2t +t, 6t} O sis a basis of P O sis not a basis of P3.

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Q: Q2. Leb u, and v be two livearly ondependent vecetors in R? Do thiy necussavily form a basis of R?

A: We have to write about vector u and v

Q: 13. Do the set of vectors S = { x²+2x-4, 6x² +7x+3, 2x²+x) a basis for P2? Refer to the definition…

A: The given set is;  S=(x2+2x-4, 6x2+7x+3,2x2+x).

Q: 1 Which of the following is a basis of R4that includes the vectors and 1 ? 1 -1 1 1 1 1 1 1 -1 1 1 1…

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Q: 3) If V = R? and neither a, c nor b, c is a basis of R2, show that c 0. %3D

A: 3. It is given that a, c  is not basis of V ⇒c=λa    it is also given b,c is not basis of V⇒c=μb…

Q: Let S = {v1, v2} be a basis of IR? where vi = and What element of R? is determined by the linear V2…

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Q: 1

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Q: 4. Let B = and observe that B is a basis for R³. Using the vectors in 3, find an orthogonal basis…

A: The solution are next step..

Q: {( a + b+c+d b – c+ 2d а + 2с — d H = : a, b, c, d e R } C R³, and consider --(}) u = 1 (а) Is u E…

A: Given, H=a+b+c+db-c+2da+2c-d: a,b,c,d∈ℝ⊆ℝ3      ⋯⋯(1) a) Given, u=111 Consider the system,…

Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. -3° 2 , 83 = S2 1

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Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

A: Since you have asked more than one question, we will solve first one for you. If you want other…

Q: Let {e1, e2, ē3, ē4, ē5, ē6} be the standard basis in Rº. Find the length of the vector 4ē4 + 4ē, –…

A: Consider the given standard basis in R6 as, e1→,e2→,e3→,e4→,e5→,e6→ As we know that standard basis…

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², –1 – 6x + 7x²} O s is linearly dependent. O…

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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Q: Which of the following is not a basis of p2? O a. ((1,3),(1, – 1)}. O b.{ (1,2), (5,3)}- OC.{(1,0),…

A: We know, any collection containing exactly two linearly independent vectors from R2 is a basis for…

Q: Explain why S is not a basis for P2.S = {−x, 4x2}

A: Given: S={−x, 4x2} To Explain: Why S is not a basis of P2.

Q: The set B = {322 – 4, 15x² – (20 + 2x), 38 + 4x – 27x²} is a basis for P3. Find the coordinates of…

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Q: -() --() --() 14. Let ei = e2 = ez = 1 3 Show that {e1, e2, e3} is a basis of R3 and write v = (66,…

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Q: The set B = {3x² – 4, 152² – (20 + 2x), 38 + 4x – 27x²} is a basis for P. Find the coordinates of…

A: Given, the set B=3x2-4,15x2-20+2x,38+4x-27x2 is a basis for P2. We have to find the coordinates…

Q: Define a basis v1, v2 of R² by vị obtained by applying the Gram-Schmidt Procedure to v1, v2? 2 by…

A: Consider the provided question, A Basis of a vector space. Let V be a subspace of Rn for some n. A…

Q: Determine whether S is a basis for P3. S= (3-t, t3, 9t2, 8t + t, -1 + 3t) OS is a basis of P3. OS is…

A: Please see the below picture for detailed solution.

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: Determine whether S is a basis for P3. S = {5 – t, t³, 4t2, 2t + t³, =1 + 5t} O is a basis of P3. O…

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Q: . ) The set B = {4x² – 4, 4x – 20 + 20z², 37 – 8z - 36x²} is a basis for P. Find the coordinates of…

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Q: - - The set B = {x² - 2, 4x² − (8 + 3x), 15x² − (28 + 9x)} is a basis for P₂. Find the coordinates…

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Q: 1 1 11

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Q: 4.13 Let {u1,u2,..., un} be any orthonormal basis of (where F R or F = C). Show that %3D Euju; = 1.…

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Q: Let V = span {1+ 2x – x² + 3r³, -2+x+x² – x*, -1+ 8r – x² + 7r", 3 + x – 2r² + r'}. Find a basis ß…

A: Step:-1 Note:- To span V we need the polynomials of degree 3, so dimension of V is 4. (think using…

Q: 4 2. If a basis for R3 is B = -3 and given [x]B find i in the standard basis.

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Q: - --- Let B = Is Ba basis ofR ? Justify and x = %3D 2 3 3 your answer. If yes, compute xR [x]

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Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent. O…

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Q: The set B = {1– 2t + t2,3 – 5t + 4t² , 2t + 3t²} is a basis of P2. Suppose C = {c1, C2, C3} is…

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Q: Explain why S is not a basis for P. S = {1, 2x, =7 + x², 9x} O S is linearly dependent.

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Q: Show that B = {1,1 – x,2 – 4x + x²,6 – 18x + 9x² – x³} is a basis for P3(R). Hint: Recall that…

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Q: Prove that B is a basis of V.

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Q: Let B = {x – 2, x² - 2,4x}. %3D Which of the following statements is true? B is a basis of P3 B is a…

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Q: Let V = span {V1, V2}, where V1 and V2 = 1 2 Find a basis S for R3 that includes vi and v2.

A: Let V  = span { v1 , v2}  where   v1= 102 and v2 = 111 Find a basis S for R3 that includes v1 and…

Q: Consider the basis B={(2,1),(-1,2)}. What are the Fourier coefficients of (0,5) w.r.t. B? (1/2,2)…

A: Given- Basis , B=(2,1),(-1,2)To find Fourier coefficients of (0,5) w.r.t. B Suppose ,  Fourier…

Q: Find a basis for the plane 4x + 3y + 5z = 0 in R³.

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Q: 23. Suppose R* = Span {v1, ..., V4}. Explain why {v1,..., V4} is a basis for R4.

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Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent.

A: Given that S=1-x,1-x2,-1-6x+7x2 Explain why S is not a basis for P2 if S is linearly dependent the S…

Q: Explain why S is not a basis for P2. S = {1, 8x, -6 + x², 3x} O sis linearly dependent. O s does not…

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Q: Determine whether S is a basis for P3. S = {6 – 2t2 + t³, -4 + t2, 3t + t³, 5t} O sis a basis of P3.…

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Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x2, -1 – 7x + 8x²} O sis linearly dependent. O…

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Q: 1- The vectors x, = (2,1, -4), x2 = (-3,4,1) and x3 = (2, –1,3) in R3, are %3D A: represent a basis…

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Q: Let S = {1+4x– x², 2+5x+3x², 3x –5x², 3+15x +8x} . Does S span P,? Is S a basis for P, ? If not,…

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Q: Use the above to answer the following questions. 7.1 Find a basis for the nullspace of A. 7.2 Find a…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.