Consider two bases B= (b, b2) and C= (c, c2) for a vector space V such that b, =e, - 6cz and by = 5e, + 2c2. Suppose x= b, • 3bz. That is, suppose (xla = .Find (xlc- OA. 16 - 17 11 OC. 15 O D. 8. 16

Q: Consider the real vector space M2x3(R) with the usual inner product (A, B) = tr (B'A) Given the…

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Q: Let D= {d1,d2, d3} and F= {f1, f2, f3} be bases for vector space V, and suppose fi = 2d1 – d2 + d3,…

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Q: Find the vector projection of onto v. u = 12i + 3jP + 4k U = i + j +k>

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A: Given below the answer

Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

A: Dimension of vector space is number of element in basis

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Q: Given the operator S on the vector space R₁ [x] given by S (a+bx) = -a+b+ (at 2b) x A) What is SC1)…

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Q: Let ƒ : R² → R be defined by A if (x, y) # (0,0), f(r, y) = if (r, y) = (0,0). Determine the nonzero…

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Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (x, , y.) +…

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Q: Let B = {bj, b2} and C = {c],c2} be bases for a vector space V, and suppose bj 3 бс1 — 2с, and bz —…

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Q: Consider the real vector space M2x3(R) with the usual inner product (А, В) — tr (B'A) Given the…

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Q: (2) Let vị = ( 2 = (2),v3 1 of the vector space R³. (2a) Does the vector v = (6 belong to…

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Q: Determine whether the set B is a basis for the vector space V.

A: V=P2  ,B={ 1,1+2x+3x2)

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A: By using definition of linearly dependent and independent.

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Q: Consider the real vector space M2x3(R) with the usual inner product (A, B) = tr (B'A) Given the…

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Q: In any vector space V, show that (a + b)(x + y) = ax + ay + bx + by for any x, y e V and any a, be…

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Q: H, ond H2 are subuedɔr spoces of vector space, Sp (H, U Ha) - H, +H2 show that I

A: Proof :-

Q: Consider the real vector space M2x3(R) with the usual inner product (A, B) = tr (B' A) Given the…

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Q: Let D = {dj, d2} and 5 = {bi, b2} be bases tor vector spaces V and W, respectively. Let T : V → W be…

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Q: Let W = Span {V1,..., v,}: Show that if x is orthogonal to each Vj, for 1 < j < p, then x is…

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Q: Let B= {b,,b2}, and C={c,,c2} be Bases for a vector space V, andsuppose b1=6c,-5c2, and b2 =3c1-2C2.…

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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.