Let fi = 1+a + 5a², f2 = 1 + 2x + 8a². B = (f1, f2) is a basis for the subspace V = {ao +a;# + azw² : 2ao + 3a, – az = 0} of Ra[r]. () Let g = -3+ 4æ + 6a². If [g]8 then s= %3D a) 10 b) 3 c) -3 d) -10 e) vector g is not in V.

Q: Let B= = (1, +2, (x - 1)², 42³) be an ordered basis for P3. Find the coordinate vector of f(x) = 1x³…

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Q: Find a basis of the subspace of R* defined by the equation 5x1 - 7x2+8x3 6х4 = 0. 9. 9. 9. Basis: 9.…

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Q: Question 1 Let W be the set of all vectors of the form a) [α] b where -2a +6b-6c = 0 Lc -3 Determine…

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Q: 3 = [2 +21 Verify Properties (vi) and (viii) in showing C²x2 is a 2+2i 4+i Let c₁= 21, C₂ = 1 + 2i,…

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Q: Find a basis of the subspace of R5 spanned by the following vectors: -7 -3 -3 + -3 7 -2 10 2 0 3 3 3…

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Q: Let Hspan {(-3,-1,-2), (17, -1, 10), (-5, 0, -3)}. A basis for the subspace HCR³ is { vector

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Q: Show that S = {t+1,t-1,(t-1)2} be a basis of P2, the vector space of all second-degree real…

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Q: Which one of the followings is NOT the subspace of R2 ? W = {(0,–2a): a e R} - W = {(2a, a): a e R}…

A: To find which one is not a subspace.

Q: Find the basis of subspace defined as S = {(a, b, c)|a - b +2c=0}.

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Q: Your answer should be a list of row vectors separated by commas. (Click vector to learn about…

A: We have to find the basis from the given form of vectors.

Q: Determine if all polynomials P = ao + a,x + a,x² + a3x³ , with ao, a1, a2, az integer, is subspace…

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Q: Show that the set S= {(-2,-4), (1, 2)} is the basis of R2 or not?

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Q: a) Give an example of subspaces U = span(f1, f2, f3) and V = span(g1,92; g3) of RaJa] such that…

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Q: Exhibit a basis for M2x2, the vector space of all 2 x 2 matrices of real numbers.

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Q: If B is the standard basis of the space P3 of polynomials, then let B = {1, t, t², 13³). Use…

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Q: b) Find the value of k such that (-1,1,1), (1,1,1), (1, -1, k) form a basis of R²

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Q: Determine whether B={1-31²,2+t-5t².1+2t) is a basis for P2.

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Q: Show that B = {v1=(1,0,0), v2=(3,7,-2), v3=(0,4,1)} is a basis for R3

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Q: 21 Find a basis for the subspace of R³ consisting of all vectors 2 such that -81 + 9x2 + 4x3 = 0 13…

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Q: 4. Find representation of the vector v = 2 – 2x+ 6x? with respect to following basis. {1+ 3x + 3x?;…

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Q: Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² +…

A: We know that two vectors are linearly dependent if one vector can be written as a scalar multiple of…

Q: 3. Let vi = [1, -2,3], v2 = [-1,–4,5], and v3 = [5,-1,3] be vectors in R³. a) Use determinant to…

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Q: Determine whether W = {ao + a1x + a2x² + a3x°|ao + a2 = az ɑ1} is a subspace of P3.

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Q: Consider the subspace 2 4 U = span{ -2 of R4. Create a basis -2 { -2 for U.

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Q: x-3x+1 7. Is the set {(1,2,-1,3), (1, -1, 2, 0), (-2, 0, 6, 6)} a basis for R¹? Justify your an-…

A: The objective of this question is to determine whether the given set of vectors forms a basis for…

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.