s = (6 4 1) (3 −5 1) (8 13 6) (0 6 9) explain why S is not a basis for R3

Q: Explain why S is not a basis for R2.S = {(2, 3), (6, 9)}

A: We know the basis of R2 = {(1,0),(0,1)} So it has 2 elements So, another basis of R2 also must have…

Q: 26. B = (f1, f2, f3) is a basis for R2[x]. If the change of basis matrix 1 3 from B to Sr, læ] is 1…

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Q: -1 Express the general solution of Ax = b where A = 3 and 3 1 as x = x, + cx, where x, is the row…

A: It is given that, Ax=b where, A=-1-133 and, b=1-3

Q: 7. Prove that p, (t) = 1+t², p2(t) = t – 3t2, p3(t) = 1 +t – 3t, is a basis for P2.

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Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

Q: Which of the following is a basis for R2? (a) {(1,-1),(-1,1)}  (b) {(1,−1),(1,1),(−1,1)}  (c)…

A: Let V=ℝ2. Identify the basis of ℝ2.

Q: -6 Express the general solution of Ax =b where A = and 6 -12 -6 as x = x, + cx„ where x, is the row…

A: Given: Matrix A=3-66-12 and B=-6-12. The objective is to express the general solution of Ax=b.

Q: 1 3 S = 4 9. a basis for R3? Explain why or why not.

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Q: [4 3 8] Q6. Write the basis and dimension of the row space and column space of A = 3 2 l2 2 2) 1.…

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Q: Complete the standard basis for R². Ex: 5 1

A: The basis of the vector space V in ℝn is the n number of linearly independent vectors which spans…

Q: Explain why S is not a basis for R3.S = {(7, 0, 3), (8, −4, 1)}

A: Basis definition:

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: 18 Given the basis B -2 1 7 7 if the coordinates of w relative to basis B are wB - 4 find w 2

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Q: prelative to the basis S=(P. P2. P3) for P2. p = 20 - 30x +25x; P, = 5, p, = 5x, ps = 5x. %3D %3D…

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Q: Explain why S is not a basis for R2.S = {(4, −3), (8, −6)}

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Q: –10 S = l2] ] 13 2. 2.

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Q: За + 6b — с ба — 26 — 2с - Find a basis for H = : а, b, с €R -9a + 56 + 3c | -3a + b+ c

A: Given H=3a+6b−c6a−2b−2c−9a+5b+3c−3a+b+c:a,b,c∈R We have to find the basis for H. First write the…

Q: Find all values of a for which {[a? 0 1]. [0 a 2].[1 0 1]} is a basis for R3.

A: let v1=a2 0 1 , v2=0 a 2 and v3=1 0 1 be the three vectors in R3. now these vectors forms a basis of…

Q: GE)- 7. If a basis for R3 is B = and given [x]B = find i in the standard basis.

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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: Let B = {1+x, 1 – x², x + 2x²} and p(x) = 7+ 10x + 11x². You are given that B is a basis for IP2.…

A: NOTE: Refresh your page if you can't see any equations. . write all polynomial as a vector

Q: Explain why S is not a basis for R2.S = {(6, −5), (12, −10)}

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Q: Explain why S is not a basis for R3.S = {(1, 1, 1), (0, 1, 1), (1, 0, 1), (0, 0, 0)}

A: To Determine S is not a basis for R3.S = {(1, 1, 1), (0, 1, 1), (1, 0, 1), (0, 0, 0)}

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.…

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Q: -2 1 4. Let v, = 4. 0 ,and v3 -4 Is {v1,V2.V3} a basis for R? V2 = %3D 0. %3D %3D -4 - 4 - 4 O No…

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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: 3 6. (c) Find B if S is the basis in 3 -12 -1 2 B = .... ......

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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: B = (f1, f2, f3) is a basis for R2[] where fi = 1+ 2x + a², f2 = 2+ 3r + 2x², f3 = 2 + x +3x². If…

A: The correct option is option (e) 1 + 2x²   The detailed solution is as follows below:

Q: Determine whether S is a basis for P3.S = {−1 + t3, 2t2, 3 + t, 5 + 2t + 2t2 + t3}

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Q: If {x, a} is a basis of solutions of a?y" + axy' + by = 0, then a = (A) -2 (в) 2 (C) -3 (D) 3 (E)…

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Q: y" + ay' + by = 0 for the given basis. -4.3x 16. e2.6x

A: We have to find the ODE for the given basis.   According to our guidelines we can solve only one…

Q: 2: Consider B= a) Show that B is a basis for R³.

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Q: 1 2 1 251 1 3 7 2 2 4 9 3 - Given A = 1 Find the basis for nullspace of A. HA 3 3. 1 a. b. С. d. 1…

A: A=121025113722493-1

Q: See picture

A: Does the set L of two vectors form a basis for the subspace S?

Q: Find a basis for (null(B))+, where 1 2 -1 -3 2 2 4 -2 1 4 B := 1 2 3 -1 -2 1 2 11 -11 -10

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Q: Lemma 2.8 B is a basis of T iff

A: To prove that Β is a basis of Τ iff ∀Ο∈Τ ∃ Β0⊂Β: Ο=∪ ΒΟ

Q: Let B = {1+x, 1– 3x?, x + 6x²} and p(x) = 12 + 8x + 9x?. You are given that B is a basis for P2. If…

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Q: = {W₁, W2, W3} is a basis for R³, where 1 3 H W2 = 3 W3 -2 -4 Determine if the set B W₁ = 2 9 = -3 A

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Q: -2 0 1] 2 1? 1 Which of the following is a basis for the column space of -1 -4 2 4 27 2 | 2 1 -1 2 2…

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Q: 10. The solution set to the equation Ax = b is 1+t1 2 - t t + u :t, ueR} when b %3D L2t· - u a) How…

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Q: 3. T: P, P, is defined by T(a, + a,x) = -a, + (a, + a,) B is the standard basis for P1, and B' =…

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Q: Find a basis for Q(3^(1/3), 3^(1/2)) over Q.

A: It is known that,

Q: (b) Find q if S is the basis in x2 + 1, x2 – 1, 2x – 1. (c) Find B if S is the basis in 3 -1 -12 1 В…

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Q: 10 2 1 4 5. Let A= 1 130 4 10 20 3 • What is RREF(A)? o Find a basis for R(A). • Find a basis for…

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Q: [7 2 4 6 What is [A]B, the coordinates of A = with respect to the standard 10 0 1 basis B = of R2x2?…

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Q: Explain why S is not a basis for P2.S = {1 + x2, 1 − x2}

A: Given: S = {1 + x2, 1 − x2}

Q: S = (1+ x, 1- 2x) is not a basis for P,(th

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.