Find a basis for orthonormal complement W- for a set W, a subspace in R* W = [2x, + x, + X + 2x, = 0 0= *x+ x- x- xf

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Q: ons are just verification how it is a vector space. with real entries under the usual matrix…

A: Given that V=ℝ3={(x1,x2,x3)x1∈ℝ} define for any α,β∈V where α=(x1,x2,x3), β=(y1,y2,y3) the vector…

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Q: The intersection of an arbitary collection of subspaces of a vector space is also a subspace.

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Q: Let X,Y be a finite dimension vector space then O dim(x)=dim(Y) O dim(X)<dim(Y) O dim(X)zdim(Y) O…

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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Q: Sui+ (v,u2)u2+ ··+ (v,uk)uk. =(v) is the closest vector to v in U and that it is the Iv - proja(v)I

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Q: Consider the subspace U = span{ of R4. Create a basis ,x) for U.

A: x=(0,-1,1,-1) will be the basis, Which can be expressed as the linear combination of U, and it is…

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Q: Find an orthonormal basis for the subspace Span ([1, 2, 0, -2], [4,3,0, 2]) of R4.

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Q: Show that a subspace of a Hausdorff space is Hausdorff.

A: Prove that, a subspace of a Hausdorff space is Hausdorff.

Q: Let (V,(*,*)) be an F-inner product space,where F is either R or C. LetU C V be a subspace and let a…

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Q: Let U_1, ..., U_m be subspaces of some vector space V. Show that U_1 + ... + U_m is the smallest…

A: ●Additive identities:0∈ U1 ,......,0∈ Um . ●Closed under addition: u1 ,w1 ∈ U1 ,....,um  ,wm∈ Um.…

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Q: The action of a projection (generating) operator a basis function always creates a normalized linear…

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Q: ༤ས་ Let A = = [3 0 0 -3 -2 -1 A basis for the null space of A is { vector

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Q: Let P3 is the vector space of polynomials of the degrees3,Consider the polynomials…

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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.