18. Which of the following subsets S is a subspace of R²? (a) S= {(x1,x2)||#1| = |r2|} (b) S = {(x1,72)|r2 = #1 + 1} (c) S = {(r1,X2) | #2*1 = 0} (d) S%3D {(zn,zz) |피3D } %3D (e) None of the above

Q: (3) For each of the following sets, determine whether it is linearly independent or dependent. (a)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 1. Consider the following subspaces of R³: U = {(x,x,y): x,y ER} and W = {(x,-x, 2x): x, y ≤ R} (a)…

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Q: 4. The dimension of space of all 7-by-7 skew-symmetric real matrices has a dimension (a) 28 (b) 21…

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

A: The given sets are  (d) x∈ℝ3:x12+x22+x32=1 (f) x∈ℝ3:x12+x22+x32=-1 (h) x∈ℝ3:x=301+s211+t121 for some…

Q: B 6. Which of the following is a subspace of R³? a. {(x,y,z)/x-3y-1} b. {(x,y,z)/x=3y+1} c.…

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Q: 1. Determine whether the set S is a subspace of V or not, where Explain your answer. S = {p(x) = P₁…

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Q: 4. Let W be the subspace of R³ spanned by w the orthogonal projection of 8- onto W. - (2/3) 1/3 and…

A: orthonormal vectors:- A set of non zero vectors v1, v2, v3,......, vn is called orthonormal if…

Q: Decide if the following subsets are: {(x,y,z) e R³: 2x + y - 3z = 1}. {(x, y, z) e R³: 2x = y + z}.…

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Q: 7. Let W span{x} be a subspace of P2(R) with (p(x), q(x)) = p(x)q(x) dx. Find W-.

A: I am solving this in step 2

Q: 6. Which of the following are subspaces of R° ? (x, y, z all bclong to R) (i) W {(x, y, z): x + y +…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 4. Determine whether W is a subspace of R³. a. W = {(x-1, x,x) x ER} b. W = {(3x, 0,-x)|x = R} 3 x 0…

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Q: 9. Determine if the following subsets of R² are subspaces of R²: (a) S = {(x,y)| xy ≥ 0} (b) E=…

A: 9.  (a) The given set is S={(x,y) | xy≥0 } . Let (1,2)∈Sand (-2,-1)∈S( Since 1×2=2>0 and…

Q: Is the set W = {f(x) = P(F) : ƒ(x) = 0 or f(x) has degree n} a subspace of P(F) if n ≥ 1? Justify…

A: Set : W= fx∈PF : fx=0 or fx has degree n

Q: 5. Let W₁ = equal to (a) 0 and W2 = (b) 1 0 be subspaces of R³. Then dim(W₁ W₂) is (c) 2 (d) 3 V

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Q: -(80) (b) 2. The subspace (a) x+y+z= By in R³ is a plane whose equation is x-2=0 (c) y x-2y+z=0 (d)…

A: Here i am using linear combination and then we saw the relation between the coordinates.

Q: (3) Is Mmxn(Q) is a vector subspace of Mmxn (R) over R?

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Q: Find a basis for the solution subspace Ax=0 where A=[-2,4; 1,-2] OA. {(1,0),(0,1)} O B. {(1,2)} C.…

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Q: Let L: R³ → R³ be the linear operator defined by L(x) = -1521 12x2 + 15x3 [25] -6x2 -45x₁ +45x3 (a)…

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Q: Which of the following sets are subspaces of R°? A. ((x, y, z) | x < y < z} B. ((x, y, z) | 5x – 9y…

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Q: What is the dimension of the sum of subspaces V and W in R3[x], where V={f∈R3[x]∣ f(0)=0} and…

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Q: 5. Let U = {(u1, U2, U3) E R3³|u₁ + u2u3 = 0} and V = {(v₁, V2, V3) E R³|v1 - 302 +503 = 0}. (a)…

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Q: One of the following sets is a subspace of P4 (a) {f(x) E P4 : f(0) = 1} (b) {f(x) E P4 : f(1) = 1}…

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Q: 1. Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1) a subspace of R*? Show the details of %3D your…

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Q: A given field mouse population satisfies the differential equation dp dt = 0.2p - 380. where p is…

A: The given differential equation is       = 0.2p - 380  =&gt;  = dt Integrating both sides, we get…

Q: Let V = R? and K = R. Which of the following are subspaces of V? Give reasons for your answers.…

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Q: -8 -5 -1 6 -4 --- U₁ = -5 -6 -7 -10 1 -18 Compute the distance d from y to the subspace of R4…

A: Given: y=-8-1-5-10, u1=-56-61, u2=0-4-7-18To find: The distance, d from y to the subspace of ℝ4.

Q: (c) H(y) = ſ2 log y'(x) dx, Y = C' [a, b]. (d) J(u) = [p/u; – u; dA; Y = C'(D), where D is a nice…

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Q: Q-3 (a) Suppose U = {(x, y, x+y, x- y, 2x) E F5 : x,y E F} Find a subspace W of F5, such that F5 =…

A: U=x,y,x+y,x-y,2x∈F5 : x,y∈ F U=span1,0,1,1,2,(0,1,1,-1,0) We have to find a subspace W of F5 such…

Q: Find a basis for the subspace of R W- (*,X,X3, X4, X )x + 2xz + Xg = 0) {(1.0.00.1).(.-1.0.0.2).…

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Q: (a) Any subspace must contain a zero vector. T F

A: Examine the given statements are true or false. Subspace: Any subset A of the vector space V is said…

Q: Determine which of the following sets are subspaces of R 1. {[x, y, 2] | - 5x − 7y + 3z = 4} 2.…

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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.