et X = {(x,y, z): Vx² + y² + z² <1} be a subspace R° with the standard topology and 0 = (0,0,0). Show that the fundamental gro

Q: Prove thatII = {(x, y, z)|x – 2y+ 3z = 0}is a subspace of JR³, %3D -

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Q: What is the dimension of the subspace H of R spanned by the given ved V1, V2 and v3 2 3 Vị = -8 V2 =…

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Q: Let F be the vector space of infinitely differentiable functions from R to R. Consider the subspace:…

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Q: Provide a counterexample to show that the following statement is false: "If U₁, U₂, W are subspaces…

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Q: 3. Let W = {(x,y,z): x? + y? = z}. Is W a subspace of V = R3? %3D

A: We need to check if W is a subspace or not.

Q: Let pu: R³ → U be the orthogonal projection onto the subspace U = {(x, y, z) = R³: x-y-z=0}.…

A: Introduction: To find a linear variety S' that projects onto S under the orthogonal projection pu,…

Q: Set V = {(x, y) | x ER, YER}. Define addition of vectors by the rule (x, y) + (x, y) = (y + y',x+x')…

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Q: Find the orthogonal projection y of y = -{-----} = նշ W = Span ŷ Ex: 1.23 2 6 onto the subspace

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Q: 3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

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Q: HConsider the vector space R° (over R) and ZcR consisting of vectors z=(z1, z2 z3), with these…

A: Given Z⊂R3, where R3 vector space.z→=(z1,z2,z3)(a) z1=0(b) z1+z2=0(c) z1+z2=1We have to check in…

Q: 6x 1 = (2)ų pue 3 – x = (2)6 hq pelves as a co to on to a los e os (26) = projy (f) Use the inner…

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Q: Consider the subspaces U = {(x,x) | x ≤ R} and W = {(0, y) | y ≤ R} of R². Show that U + W is a…

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Q: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

Q: Show that U = {(x, y, z)|x – 2y − z = 0} is a subspace of R³.

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Q: Find a vector-valued function, using the given parameter, to represent the intersection of the…

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Q: Suppose U = {(x, x, y, y) = F¹: x, y € F}. Find a subspace W of F4 such that F4 = UW.

A: Our objective is given below:

Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

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Q: Prove that the dual of l° is not isometriç to, 1', but contains a proper subspace that is isometric…

A: Consider that there are bounded functions on l∞ which are not of the form fy=∑xkyk for some x. Let,…

Q: Which of the following sets is not a vector subspace of p? OA. W = ((x,y)x = 2y} O B. W - ((x,y)y-…

A: Subspace of a vector space

Q: HIf vectors x, y, z, u in the real vector space p (the polynomials) are defined by x(t)=1, y (t)=t,…

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Q: 4. Find an orthonormal basis for W+, where W is the subspace of R' spanned by the vectors (-1,…

A: To find- Find an orthonormal basis for W⊥, where W is the subspace of ℝ4 spanned by the vectors -1,…

Q: Consider the vectors v1, v2, ..., Um in R". Is span (01,..., īm) necessarily a subspace of R" ?…

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Q: Find a basis and the dimension of the subspace of R³: W = {(x, y, z): x - 2y + 3z = 0}

A: The given subspace of ℝ3, W=x, y, z|x-2y+3z=0. We have to find the basis and dimension of the…

Q: Let S € R² | xy ≥ 0 Y where S uses the usual definitions for vector addition and scalar…

A: Given subset of is the following :Obviously Here noted that vector addition rule : and scalar…

Q: Is W = ((x,y) | xy=0} a subspace of R??

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Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

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Q: Consider the set ? = ((x, x+ y, 2y)|x,y are real) of vectors in r3 . Is W a subspace? If yes, prove…

A: We have Set S = {(x, x + y, 2y) | x, y are real}. Let u, v be any two element of S then,

Q: Consider the set S = yl E R : 4x +6z=7y, x – 13y=0 . Is this a subspace of R ? Explain why or why…

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Q: { 0, 1, sin’t, cos t, cos 2t } COS a cubcnnco? Juctifu vour

A: This is a question of linear algebra and vector space.

Q: 4. Consider the vector space RR of functions f: R R. Let U = {f: R → R: f(42)=0}. Show that U is a…

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Q: Show that the set (a cos (r)+bx+cla, b, c E R} is a subspace of the vector space of continuous…

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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.