1. Let V be the vector space over R, consisting of all complex polynomials of degree at most 2; i.e. V = {ao + a₁ + a₂z² | a₂ € C}. (a) Find a basis for V. Give proper reasons. (b) Find the dimension of V.

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Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: 2. (a) Find all vectors v in two dimensions having |v| = 5 such that the i-component of v is 3i. (b)…

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Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: (a) Find the vector Q=[0, a,0] such that the resultant of the vectors: P=[5, 7, 8], Q=[0, a, 0] , R=…

A: Hey, thanx for your question. According to our policy I m answering question first. Please post the…

Q: Let V be the vector space of functions spanned by B = {b₁ = 6 sin x + 7 cos x, b₂ = 5 sin x + 3 cos…

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Q: In P2 (polynomials of degree s2), let v =1+x+2x, v, = 3- 2x +x', Determine whether the vector v…

A: Let's find.

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Q: Consider the vector space V defined by V = {(x, y, z) | x+y+z=0}. Let u = (1, -2, 1) and v = (3, -1,…

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Q: Consider the vector space V over the real numbers, consisting of all polynomials of degree less than…

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Q: (1) Let x and y be the vectors x = and y = 4 (la) Find a vector z such that ||z|| = 1 and z is…

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Q: a. u + v=v+u b. (u + v) + w = u + (v + w) C. U+0=u d. u + (-u) = 0 e. c(u + v) = cu + cv f. (c +…

A: Given query is to simplify the expression.

Q: The vector x = H vector [2]8 = [2] A 1 B2 C3 in R² relative to the orthogonal basis B = What is the…

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Q: Given basis B = {(1, -1), (2, 3)} and basis C = {(1, 0), (0, 1)}, and linear map T = (x + 2y ; 2x -…

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Q: 2.3 Determine a scalar e so that the vectors a- and b-<3, c, 2e are orthogonal.

A: given that,a and b are orthogonala=&lt;5,c,-4&gt;b=&lt;3,c,2c&gt;find the value of c?