(a) Which rules are broken if we keep only the positive numbers x > 0 in R 1 ? Every c must be allowed. The half-line is not a subspace.(b) The positive numbers with x + y and cx redefined to equal the usual xy and xc do satisfy the eight rules. Test rule 7 when c = 3, x = 2, y = 1. (Then x + y = 2 and cx= 8.) Which number acts as the "zero vector"?

Q: The subset in the form where x and y are real numbers, is a subspace of R2 if Select one: O x + 0…

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Q: If v1 and v2 are in R" and H=Gen{v1, v2}, then H is a subspace of R" Justify

A: Given that : and are in  Let Now, we  have to recall  the definition of subspace of a…

Q: What is the dimension of the following subspace of R³? Justify your answer. (6.0.0 span

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Q: Please go through each option with explanation

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Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x² + x² +…

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Q: A subspace always contains the zero vector.

A: True Because of subspace is a nonempty set.

Q: -4 ---------0 3 V2 -5 and 8 in the subspace of R³ generated by V₁ and V2. 5. Let 2 -5 8 -9 Determine…

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Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

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Q: The integers 1 through 36 (inclusive) are used once each as the coefficients for six vectors in P 5…

A: We know that, A subspace is a vector space that is contained within another vector space. So every…

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

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Q: Determine whether each of the following sets are subspaces of R³ with the standard operations. sure…

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Q: 4. Use the definition of a subspace to prove that the set V:= :, y, z E R, y+ : 0 is a subspace of…

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Q: Draw Figure 4.2 to show each subspace correctly for A = and B = 36 3

A: Given matrix is .Here A is a linear map from  to  . So, we get n=m=2.Find the row space of A:Find…

Q: Is it possible to solve it using words like claim as my professor did in his example in other photo?…

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Q: Let P₂ be the vector space of all polynomials of degree 2 or less, and let II be the subspace…

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Q: 2.3.2. Show that -3 7 6 1 6 -00-0 and 3 4 is in the subspace of R4 spanned by 4 6

A: We need to solve span of vector problem.

Q: -F -5 8 generated by v₁ and v2. 3. Let vi 2 3, V₂ = -5 and w = 8 B 2 Determine if w is in the…

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Q: Determine whether W= [(a, a, b)la, bεR] is a Subspace of R³

A: Given that,  W=a,2,b|a,b∈R

Q: Let V₁ = 1 -1 3 4 Choose the correct answer below. 11 10 and w= 4 1 9 Is w in the subspace spanned…

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Q: Let M3,3 denote the vector space of all 3 × 3 matrices. Let L3,3 denote the set of all lower…

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Q: Q6: Explain whether the following sets are not subspaces of R" for the appropriate value of n. a a a…

A: We have to show that given set are vector subspace or not

Q: Consider the subspaces U = span{[4 0 1],[4_1 −4]} W = span { [-5 3 3], [-5 3],[−5 4 −2]}

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Q: Determine if v is in the subspace of P3 given by span{x + x - 5, x2 + 2x + 1, x-x2 + x}. v = x? + 2x…

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Q: 2. The subspace in R3 is a plane whose equation is x+y+z=0 x-2=0 x-2y+z=0 (a) (b) 2-0 (c) y-2--0…

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Q: -5 -4 -3 -2 -1 n y = دیار 2- 7 1 -2- -3- -4 2 3 4 10 5 Write an equation for the function graphed…

A: Given graph

Q: Select one: a. S={ X2 %3D b. , X €R} S={ 1 C. X 1 X1=2x2} X2 O d. S={ X1=X2}

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Q: 1 3 6. 3 Let vị U2 = 1 U3 = 1 and w = | 2 2 Is w in the subspace spanned by{v1, v2 , V3}? Why ? Yes,…

A: Given v1 = 10-2v2 = 311v3 = 612w = 321 The equation x1v1+x2v2+x3v3=w will have a solution if the…

Q: There is a partial insurance policy that pays $80,000 upon the bad drought state (and $0 in the…

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Q: -10 2 -+-+- = -3 8 ) Given : -5 B-B and -4 6 -34 find the closest point to in the subspace W spanned…

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Q: Given that = 2 = -------- y = V3 = 3 10 and h -12]

A: As per the guideline, I am supposed to solve only first question from the given problems.

Q: Q4. Check the following set is a subspace of R3 or not U = ((x1, x2,x3)| x, = v2 x} %3D

A: The given subset of ℝ3 is: U=x1, x2, x3 |x2=2x1 Definition: Let W be a subset of the vector space V.…

Q: Given 7: -9 -10 0 find the closest point to in the subspace W spanned by -5 -6 -4 and 64

A: We have to find out the closest point of  in the subspace W spanned by Here noted that ,let,So…

Q: The set of all 3 x 3 matrices of the form 1 0 0 0 1 0 00 -a Select one: True O False + 13x3 where a…

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Q: 6. If W₁ and W₂ are subspaces of V and dim W₁ (a) W₁ = W₂. (c) W₂ C W₁. dim W₂, then (b) W₁ C W₂.…

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Q: 2. Determine whether each set described is a subspace or R2. Justify your answer. H (a) The set of…

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Q: Let A be an n x n matrix, let S (ü, , ) be a set of non-zero vectors in R", and let U be a subspace…

A: Please see the below step.

Q: 14) Find all values of h such that y will be in the subspace of 3 spanned by v1, v2, v3 if vị = 2,…

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Q: Show that the set W is a subspace of M3x1 using the Subspace Test.

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Q: Show that the set of all polynomials of degree at most 3 forms a subspace of Pn.

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Q: Suppose B is a 5 x 5 matrix and Nul B is NOT the zero subspace. Do you have enough information to…

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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.