Let S-((0,-1,1).(0,-2,-1).(1,1.2)}. Which of the following is true?* S is not a basis for R3 S is a basis for R3 because S is linearly dependent O the above is true the above is true S is not a basis for R because S does not span IK R None of these the above is true

Q: Explain why S is not a basis for R3. S = {(4, 1, 6), (13, 6, 8), (-5, 1, 3), (0, 4, 6)} O sis…

A: To find why S is not a basis for ℝ3 where S=(4,1,6),(13,6,8),(-5,1,3),(0,4,6)

Q: Which of the following are a basis for the orthogonal complement of the span of (1,-2, -5, 1)7 and…

A: NOTE: Refresh your page if you can't see any equations. . write both vectors in the matrix

Q: 5. Let ū = (0,2, 1), ở = (-1,0, 2) and w = (2,3,0). Find the coordinates of (2,2,2) with respect to…

A: This question is related to vector space. Solve in 2nd step .

Q: If A = {v1, v2, ..., vn} be a basis for FV and n ≥ 2 then, is B = {v1+v2, , v2+v3, ..., vn+v1} also…

A:

Q: Explain why S is not a basis for R². S = {(-6, 2)} OS is linearly dependent. S does not span R². OS…

A:

Q: (16v2,2v2) is any B = {(, -),,)} be an orthonormal basis for R. If Let vector in R, determine the…

A:

Q: Which of the following set of vectors form a basis for R^2 space? 2 points O (0, 5), (0, 3)} O (1,…

A: Consider the one by one set of vectors to determine which one is the basis of R2 Space. Take the…

Q: Explain why S is not a basis for R3. S = {(-5, 1, 3), (4, 1, 6), (13, 6, 8), (0, 4, 6)} %3D O sis…

A: The given set S=-5,1,3, 4,1,6, 13,6,8, 0,4,6

Q: W= Sp { (2,0,-1,2), (d,d, 2,3) } cR find a basis for the oahogonal complement of the Ssubspace w

A: Given below the detailed solution

Q: 64 = (-12), v = (24) € M₂2 0 M22. Let u = 5.1 Write w = -3 2 -5 2 as a linear combination of u and…

A:

Q: 7. Let S be the set S = a) Show that S spans R3 and find a basis for R3 contained in S. b) What are…

A: Given :  The given set is,   S = 1-20, 012, -568, 1-21  To find : (a) We have to show that  S spans…

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 -…

A:

Q: B=[(1, 2, 1)", (0, 1, -1)', (1, 1, 1)"] is an ordered basis for , C =[(1, 1)', (2, 3) '] is an…

A:

Q: Explain why S is not a basis for R3. S = {(1, 4, 6), (6, 13, 8), (1, –5, 3), (0, 8, 3)} O s is…

A:

Q: -3' 2, uz [3] -4 is an orthogonal basis of R3 and x = 2 Let u1 1, u3 4 If x can be expressed as a…

A:

Q: 3. Let A {v1, v2, ..., Vn} be a basis for pV and n 2 2. Is B = {v1 + v2, , v2 + V3, ..., Vn + Vı}…

A:

Q: Let ={t?-1, t²-t, -t?+t-2} be a basis for P,(R). Then the coordinates of p(t)=6t2-3t-1 are [p]= %3D

A:

Q: The vectors x1 = (2, -3, 1), x2 = (1, 4, -2), X3 =(-8, 12, –4), x4 = (1, 37, -17), and x3 = (-3, -5,…

A:

Q: Let A = {v1, v2,.., Vn} be a basis for FV and n > 2. Is B = {v1 + V2, , V2 + V3, ..., Vn + v1} also…

A:

Q: If a, az, az is an orthogonal basis for R and b = a,a, + aza, + agaz then afai eTa and find the…

A:

Q: Explain why S is not a basis for R. S = {(-6, 4)} O s is linearly dependent. O s does ot span R. O s…

A: We will explain the reason.

Q: Find the coordinates of (2, 3, 4, – 1) with respect to the basis B = {(1, 1, 1, 2), (1, –1, 0, 0),…

A:

Q: sdasdw3g

A:

Q: Determine if W1 is a basis for R' and check the correct answer(s) below OA. W1 is a basis. B. W1 is…

A: A subset S of a vector space V is called a basis if S is linearly independent. S spans V.   A…

Q: 2. Let ū = (-1, 2, 1), ở = (1, – 1,–1) and w = (2, 3, 0). Find the coordinates of (2,4,4) with…

A: Using gauss Jordan elimination method to find the value.

Q: Explain why S is not a basis for R3. S = {(1, -5, 3), (6, 13, 8), (1, 4, 6), (0, 5, 7)} O sis…

A:

Q: Is R={(2,0,1), (2,-1,1), (4,2,0)} a basis for R²? Yes or No? Justify or give/find a counterexample.…

A:

Q: Let A = {v1, vz, - also a basis for pV? How about the converse, i.e. if B is a basis for FV, is A…

A:

Q: is a basis of then the second coordinate of the vector (3.5,7) in the basis B is: If B=((1,1,1),…

A:

Q: Find a standard basis vector that can be added to the set (v1, v2} to produce a basis of R^3.   v1…

A: The set (v1, v2} to produce a basis of R^3.       v1 = (1, -1, 0) and v2 = (3, 1, -2)

Q: 5. Do the vectors form a basis for R" ? If not a basis, can the vectors be used to find a basis for…

A: Check whether the given set of vectors form a basis of ℝn.

Q: Let A = {(1,0,-2); (2,1,0); (0,1, –5)} . Then A is a basis for %3D

A: set A contains 3 vectors  So, A is a basis for R3.

Q: Consider linear mapping A E L(Vn) and two basis X, Y of Vn. Select all true statements. Let Y be a…

A: Given that, Vn→vector space X=x1, x2, … , xn; Y=y1, y2, … , yn bases of Vn. A∈LV Verify the given…

Q: 5. Determine whether the following three vectors v, = (1, 2, 3, 4), = (0, 1, 0, -1) and v, = (1, 3,…

A: To determine the given vectors form of basis for or not.

Q: Explain why S is not a basis for R2. S= {(3, 5), (1, 0), (0, 1)} O sis linearly dependent. O does…

A: The given set S=3,5, 1,0, 0,1

Q: 3. Suppose that {v1, v2, V3} is a basis for V and p:(v;) = dij. Let %3D W1 = 2v1 + v2, W2 = v1 -…

A:

Q: 8. Let W = Span{v1, v2}. Find an orthonormal basis for W. Vị = -2 , V1 = 4 2

A: An orthonormal basis for an inner product space V with finite dimension is a basis for V whose…

Q: Determine whether or not the set of vectors S-(. l where -(1,1.1), - (1,2.3).-(2,-1,1) form a basis…

A: The subset S is basis of vector space Rn over field R if  S spans Rn and  S is linearly independent…

Q: 4 Let the basis for W is -5 -1 then the orthonormal basis for W is 1 2 3 a) 1 3/2 3/2 1 3 b) 3/2 3/2…

A: Othonarmal basis for the given basis, using Gram-schmidt Ortho normal basics form

Q: Explain why S is not a basis for R. S = {(6, 8, 13), (1, 3, -5), (1, 6, 4), (0, 8, 7)} S is linearly…

A:

Q: Let W = span{(1,1,-1), (2,3,1), (5,6, -2)}. i Find a basis for W. ii. Determine whether the vector X…

A:

Q: 4. Show whether the given vectors (1,0, 0), (0, 2, 0), (0, 0, 3), and (1, 1, 1) form a basis for R.…

A:

Q: 3.) 3=t(2,5,-3,-3),(-2,;3,2;2) (1,3,2,3), 1-5,3,2)3 Find o basis for Hhe Subs poce of R sponned by…

A:

Q: -900 4. 6 1 3 1 Let V = span Which of the following set is a basis for V? 2 2 3. -1 -1 1 -1 -1 -1…

A:

Q: 3 Determine if Wị is a basis for R’ and check the correct answer(s) below. OA. W, is not a basis…

A: Yes. W1 is a basis of R³.  Because, W1 consists of the linearly independent vectors [1 0 0]t , [1 1…

Q: -{圈[} B O B is an orthonormal basis for R?. O B is an orthogonal basis for IR?, but it is not…

A: Given B=1/21/2,1/2-1/2

Q: Let u = (1, 2, -1), v = (6, 4, 2) € R³. 5.1 Write w= (-3,2,-5) as a linear combination of u and v.…

A:

Q: Explain why S is not a basis for R2. S = {(-4, 2)} O sis linearly dependent. Os does not span R. S…

A:

Q: S-{(1,1,0), (-2, 0, 1), (-1, 1, 1)}is Not a basis of R O this is true O Linearly Independent Basis…

A: Let V be a vector space over the field F, then a set S of vectors of V is said to form a basis of V…

Q: Select all that apply: The set {01,..., T4} a basis of R4. There is not enough information to…

A:

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.