a Q.8. Let the set H = :a² +b >1 b Is set H a vector space? Justify your answer.

Q: a. (a+ (а x b)) Choose... (a x b) + (b x a) Choose... аx (а.b) Choose... а. (а х b) Choose...

A: It is vector calculation

Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

Q: In order for vectors and t- 3 in a vector space R3 to be linearly t+4 in depen den t what should t…

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Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

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Q: V = {ax³ + ax² + bx − 2c|a + c = 0, b ≤ R} ≤ P3.

A: Solution

Q: 3. For each set below, circle "YES" if it is a vector space, or circle "NO" if it is not a vector…

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Q: Consider the set V of all vectors of the form (x y z)T where x, y and z are real numbers. 3. Show…

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Q: Find the dimension of the vector space.R3m

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Q: 2. ( eMsa lan--a22 3. All 2-tuples representing points in the first quadrant of the plane including…

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Q: 5. Let S = {V₁, V2,..., Un}, n ≥ 2 be a set of nonzero vectors of V. Each of the following…

A: Given,  S= { v1 , v2 , v3 , ...... ,vn } , n>=2 is a set of nonzero vectors of V .

Q: _et a₁ = -1 a₂= -7 -7 3 and b = 3 -15 h For what value(s) of his b in the plane spanned by a, and a

A: If b is in the plane spanned by a1 and a2 then b can be written as linear combination of  a1 and a2…

Q: Determine the dimension of the vector space given by -a V = | a,b E R a b

A: Given V = -aa0, -b0b | a, b ∈ℝ

Q: Is the set of (infinite number of) vectors { (0,0,c) }, where c is a real number, a vector space…

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Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

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Q: 3. Let v, and v2 be vectors in an inner product space V. Show that ||v + v2||? < (||Vvl+ ||v2||)?

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Q: Can someone help me answer this question with all the steps thank you.

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Q: Let a, 1 1 -7 -7 3 and b = 3 15 h For what value(s) of h is b in the plane spanned by a, and a₂?

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Q: The Hamacher product is the t-norm given by ab t(a,b) = a +b – ab Show that this function satisfies…

A: Here the Hamacher product is the t-norm given by t(a,b)=aba+b-ab We have to show that this function…

Q: be rational numbers. Show that R is a vector space over the rational numbers Q, using standard…

A: We proved all the properties of a vector space.

Q: Determine whether the set {0.0-0} is linearly dependent or linearly independent. Justify your answer…

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Q: 11. Find the rate.cf.changf.f.at.P.in.the directod then.vectoe ūf a. f.=ylnx. P(1,-3. --3 P.(I,-3..…

A: Directional derivative

Q: Are all functions from one vector space to another linear?

A: Let f: V→W is a  map from vector  V to W such that fx=x2 The given example the function from one…

Q: Describe the zero vector (the additive identity) of the vector space. P3 x + ]+² +

A: We have to describe the zero vector (the additive identity ) of the vector space P3.

Q: X + x, + 3x, = 0 Given this system of equations: 2x, + x, +4x, = 1 3x, + x, +5x, = 2 %3D a. Find the…

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Q: V = {ax² + bx + 3|a, b ≤ R} ≤ P2.

A: Given: V=ax2+bx+3 | a, b∈ℝ⊂ℙ2 To write: The given set as span of minimum number of vectors.

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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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.