Determine if - w = {-2 5 |} -2 4 is a basis for R³. Justify your answer.

Q: Explain why S is not a basis for M2,2.

A: Let's check if S is linearly independent or not. S will not be linearly independent if for some…

Q: Q8) Explain why S is not a basis a) S = {(2,1,–2), (–2, –1,2), (4,2, –4)} for R³ b) S = {2,2,x +…

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Q: Determine if (f1, f2, f3, f4, f8) is a basis of R4[x].

A: Given:    f1=1+x+x2+x4f2=x+x2+x3+x4f3=x+2x2+x4f4=1+3x+4x2+2x3f8=1-x2 Check {f1, f2, f3, f4, f8} is a…

Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x²,1 + x + 4x²,1 – 7x

A: Consider the polynomials: 1-3x+x2, 1+x+4x2, 1-7x To show that the following polynomials form a basis…

Q: 2. Show that the following is a basis for M, 2x2 [3 6 3 1 0 -1 2 -8 12

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

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

A: Basis definition:

Q: 2) Let T a d 11 la + 2b + (-6) c + 2d + (-18) e 2a + 5b+ (-14) c + 6d+(-46) e Then a basis for…

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Q: The set B = {4x? - 1, z -3+ 12z2, 12 – 3x 40x} is a basis for P2. Find the coordinates of p(x) = 52…

A: write each polynomial as a vector  4x2-1=x2x140-1 12x2+x-3=x2x1121-3 -40x2-3x+12=x2x1-40-312 write…

Q: 1. Show that the following is a basis for R4:

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Q: Determine whether S is a basis for P3. S= {5 – 312 + t2, -4 + t2, 3t + t³, 6t} O is a basis of P3. S…

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Q: Determine whether {v1, v2, V3} is a basis for a3. R V1 4, v 2 = V 3 = -4 8 -8 -24 Yes No

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Q: Determine if 3 W = { |-4 2 |} 3 -5 %3D 3 4 -2 is a basis for R. Justify your answer.

A: Given set, W=1-43,03-1,3-54,02-2. To check W is a basis for R3. To check W is a basis, we have to…

Q: Determine whether the set {x2 + 2x - 3, 2x2 + x - 1, 3x2 + 2x - 2} is a basis for P, by solving the…

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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: Is the set {(1,0, -1,3), (1,0, 2,0), (2, 1,0, 3), (0, 1, 2, 3)} a basis for R? Justify your answer.

A: We have to show set is a basis for R4  .

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

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Q: Define po, P1, P2, P3 E P3 so that po(x) = 1, P1(x) = x, p2(x) = x² and p3(x) = x³ for all x E R.…

A: Given that  p(x)=-3+7x+2x^2

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

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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: 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: Show that the following set is not a basis of R4: 1 3 2 2 3 15 1 -3 2 -17 2 -3 13

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

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Q: 4. * Determine if the set B is a basis of R. 4a) B= 4b) B=

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Q: Consider the basis B = {H: G}: 2 [x]g = | , what is x? * - ] O a. O b. None of the answers is…

A: [X]B = coordinate of X with respect to B.

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

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Q: Use the standard basis for P2, B = {1, t, t²}, and the coordinate mapping to show that 10 – 12t –…

A: The solution is below.

Q: - 3x3 + 7x4 = 0 X1 -7x2 - 4x4 = 0

A: The solution are next step is..

Q: Determine whether the set S = {4 – t, t³, 6t2, 3t + t³, –1+ 4t} is a basis for P3. Justify your…

A: We need to determine whether the set S={4-t, t3, 6t2, 3t+t3, -1+4t}

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

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Q: See picture

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

Q: R4 Span {v1,..., V4}. Explain why {v1,..., V4} Is a basis for 4

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Q: Find the canonic analytical expression of the following quadratic form q: R³ → R, q (x) = 6x,²+x,² –…

A: Given quadratic equation is…

Q: The set { (-2, 5) , (1, -1) } is a basis for R2 Select one: O True O False

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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: The set B = {4+ x2, 12 – 4x + 3x2, 12x - 31 – 8x2} is ab rdinates of p(x) 75 – 24x + 19x? relative…

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Q: Determine whether (V₁, V2, V3) is a basis for R³. V₁ = No O Yes V₂ = 8 s 3 V3 -2 [-7]

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Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x?,1 + x + 4x²,1 – 7x

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Q: Find the standard basis B, of Eg for the polynomial q(s) = s + 4s2 – 3s – 18.

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Q: Determine whether it is a basis. S= {4 – x, x³, 6x², x³ + 3x, 4x – 1}

A: No it is not a basis  see below the explanation

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: Determine if -4 } 1 W = { 2 -5 -3 6. is a basis for R’. Justify your answer.

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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: Explain why S is not a basis for M2,2.

A: The set is S=1000,0110,1001,8-4-43   Known fact: A set of vectors S=v1,v2,…vn is a linearly…

Q: a)show that { d,b',7} it's a basis

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Q: Q8) Explain why S is not a basis a) S = {(2,1,–2), (-2,–1,2), (4,2, –4)} for R3 b) S = {2,2,x +…

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Q: What dimension is P3 (the set of polynomials degree 3 or less)? Which of the following sets form a…

A: ANSWER :

Q: Consider the following. V = P2, B = {1, 1 + 4x + 7x2} Complete the following statements. The…

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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.