Find bases of the kernel and image of the orthogonal projection onto the ry-plane in R*. basis for the kernel is basis for the image is

Q: In an n-dimensłonal unitary vector spaee V the dot product of the coordinate vectors of any iwo…

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Q: 2, Xz} is a basis of V, (R). show that {, +X, X2 + X3, X3 +Xi} is also a basis of V, (R),

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Q: Find a basis for the plane 4 + 3y + 5z = 0 in R. %3D

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. 3 S = span 4

A: In this question, we find the orthogonal set of basis by the Gram-Schmidt process.

Q: Find an orthonormal basis for the colspace(A) when A = [1 1 -1 3 4 4 1 1 0]. Make sure that you show…

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Q: 4. Prove that ū = (1,0, 1), ở = (2, 2, –1) and w = (-2,3,0) are a basis for R. Use these three…

A: Given u=(1, 0,1), v=(2, 2,-1), w=(-2, 3,0)  To check they form a basis for R3 or not.

Q: The set B= {(1,0, 1), (0, 1, 2), (2, 1,0)} is a basis of R Use the Gram-Schmidt process to transform…

A: Given, Basis is,

Q: 14. a) Use the Gram Schmidt Orthogonalization Procedure to transform the basis {(0, 1, 2), (1, 1,…

A: The given basis of for R3 is 0,1,2, 1,1,2, 1,0,1

Q: Orthogonalize the basis {(1, 1, 1, 1),(1, 1, −1, −1),(0, −1, 2, 1)} by the Gram-Schimidt process.…

A: Let x1 = 1111 ; x2 = 11-1-1 ;  x3 = 0-121      Using Gram schmidt process , we get orthogonal…

Q: 13. Do the set of vectors S = { x²+2x-4, 6x² +7x+3, 2x²+x) a basis for P2? Refer to the definition…

A: The given set is;  S=(x2+2x-4, 6x2+7x+3,2x2+x).

Q: Find a basis of the subspace of IR" that consists of all vectors perpendicular to both 0. 1. and -69…

A: The given vectors are  v1=10-17   and  v2=01-94  Let the vector in R4 of the form u=abcd   This…

Q: Find a basis for the space spanned by these vectors:

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Q: 3. Consider R with the standard inner product (i.e. the dot product). Let U = span Find a basis for…

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Q: Find a basis for the set of vectors in ℝ2 on the line y = 5x.

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Q: 11. Consider the vector space generated by [1, 1,1, 1), [1, 1, 2, 4), (1,2, -4, –3). Find an…

A: Note: according to our guidelines we can answer only 11 th question

Q: 14. Use the Gram-Schmidt process to transform the basis for the Euclidean space R" into an…

A: We have to transform the given basis into an orthonormal basis for ℝ3

Q: Let S ={v1 , v2 ,...,vk } be an orthonormal basis for the Euclidean space V and {a1 ,a2 ,...,ak } be…

A: Given: S=v1,v2,,....vk is an orthogonal basis for the Euclidean space V. Also, a1,a2,...,ak is any…

Q: Assume that the vector space R' has the Euclidean inner product. Apply the Gram-Schmidt process to…

A: The given vectors u1→=1,1,1, u2→=0,1,1, u3→=0,0,1

Q: The given vectors form a basis for R2 or R3• Apply the Gram-Schmidt Process to obtain an orthogonal…

A: Given data:     The given first matrix is: . The given second matrix is: .   The expression for the…

Q: 3. Consider R³ with the standard inner product (i.e. the dot product). Let {(} 1 1 U = span -1 1 2…

A: First we find the orthogonal basis of U, then find the third vectors which is orthogonal to the…

Q: 2 Find an orthogonal basis for the space spanned by 4 and

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Q: The given vectors form a basis for R2 or R3• Apply the Gram-Schmidt Process to obtain an orthogonal…

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Q: The given vectors form a basis for R2 or R3• Apply the Gram-Schmidt Process to obtain an orthogonal…

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Q: The Gram-Schmidt process transforms the basis u,=(1, 3), u,=(1, –7) of R² into the orthogonal basis…

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Q: 4. Let R³ be equipped with the dot product and let B = {(1, 1, 1), (0,2,0), (2,0,1)). B is a basis…

A: Gram-Schmidt Theorem to find orthogonal basis: Let {a1,a2,a3} be the basis of a vector space V and…

Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

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Q: Let u2 u3 be a basis for R. Use the Gram-Schmidt process to find an orthogonal basis under the…

A: Here to find value of constants first we have to find out orthogonal basis using Gram-Schmidt…

Q: Let R* have the Euclidean inner product. Use the Gram-Schmidt process to transform the basis {u1,…

A: use the Gram Schmidt process to transform the basis to an orthonormal basis.

Q: find a basis for the kernel of the transformation and give its dimension

A: T:P2R→M2×2Tf=df0dx2f00d2fsdx2f is a polynomial of degree 2.

Q: The union of these two orthogonal bases (put the basis for W and W- into one set) is an orthogonal…

A: Since you have asked for part (d) and (e) , so i answered here only for part (d) and (e).

Q: In an n-dimenslonal unitary vector spaee V the dot product of the coordinate vectors of any two…

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Q: Apply the Gram-Schmidt orthonormalization process to transform the given basis for R into an…

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Q: Every vector in a space is orthogonal to the zero vector of that space. Every orthonormal basis is…

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

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Q: Suppose V = P2 with the inner product p(x)q(x)a Apply the Gram-Schmidt orthogonalization process to…

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Q: Use Gram-Schmidt to find an orthogonal basis for R' if B={(2, -5), (1, 3)}.

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Q: The vector space V over R has a basis {u, v, w}. The linear map o : V → R² has the property that…

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Q: Let {v1, ... , vn} be an orthogonal basis for Rn and let W = span(v1, ... , vk)· Is it necessarily…

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Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

A: Given that V be the vector space of polynomials of degree ≤2 with real coefficient, endowed with the…

Q: What are the spline basis functions for a cubic spline basis with 3 knots at values x1, x2, and x3?

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Q: 2. Let the inner product on vector space V be (u,v)= uvdz. Use the Gram- Schmidt process to…

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Q: Use Gram-Schmidt to find an orthogonal basis for R if B={(-5, 2), (3, -1)}.

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Q: Let {u₁, U2, u2} be an orthonormal basis for an inner product space V. Suppose v = au₁ + bu₂ + cuz…

A: We have v=au1+bu2 +cu3 Now, ∥v∥=a2+b2+c2 Given ∥v∥=80 So,  80=a2+b2+c2⇒802=a2+b2+c2⇒80=a2+b2+c2…

Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. S = span 1.

A: I am going to find the orthogonal basis for S by using the Gram-Schmidt process.

Q: Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an…

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Q: Let S = {u1, u2,..., uk } be an orthonormal basis for a subspace W of Euclidean space V that has…

A: given S=u1,u2,.....,uk be the orthonormal basis for a subspace W let V=V1,V2,......,Vn be the…

Q: An orthonormal basis relative to the Euclidean inner product is given. 5 = {v, V2, …', Vn} is an…

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Q: Find the standard matrix for the stated composition of linear operators on, orthogonal projection on…

A: Reflection Matrix about the xy-plane is : Rxy=10001000-1 Reflection Matrix about the xz-plane is :…

Q: Find bases of the kernel and image of the orthogonal projection onto the plane -5æ – 5y + z = 0 in…

A: Given the plane is -5x-5y+z=0 in ℝ3. Solve -5x-5y+z=0 for z: -5x-5y+z=0z=5x+5y Any vector in ℝ3 is…

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.