let b={(0,2,-2)(1,0,-2)} be a basis for a subspace of R^3 and let x=(-1,4,-2)  be a vector in the subspace. find the coordinate matrix of x relative to B. use the GRAM-SCHMIT orthonormalization process to transform B into an orthonormal set B'. find the coordinate matrix of x relative to B'.

Q: Which of the following sets is a basis for the subspace U={(a,b,c,d)∈R4 ∣ a−b=0,a+d=0,b+d=0} in the…

A:

Q: Give an example of a non-zero subspace of R^4 which has dimension > 1 and does not contain any of…

A: Consider the example f(x) = {2 + x + x2}, this given polynomial has dimension 3 with the basis {1,…

Q: Let V be the vector space V = Span(e^(2x) , e^(3x) ). Given are the ordend basis defined by: B =…

A: This is a problem of Vector Analysis. One can take it as a problem of Line

Q: Determine whether or not the matrix  {(2) , (3)} is a basis for R^2…

A:

Q: For each matrix A below, describe the invariant subspaces for the induced linear operator T on F^2…

A:

Q: Let the basis {(1,1,0), (0,1,1), (1,0,1)} of the space R^3 be orthonormal in the scalar product…

A: {Here we use  a•(b+c) = a•b +a•c}

Q: Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: The given vectors are                                   -3110, -12613, 3-55-6, -33-23…

Q: find an orthogonal basis and then an othnormal basis for the subspace U of R3 spanned by v1 =…

A: The objective of this question is to find an orthogonal basis and then an orthonormal basis for the…

Q: Find a basis for the subspace spanned by the given vectors. What is the dimension of the subspace? 1…

A:

Q: Use the inner product (u, v) = 2u;v, + uzv2 in R2 and the Gram-Schmidt orthonormalization process to…

A:

Q: 4. (i) Let v1 = 〈1, 2, 0, 3〉 , v2 = 〈4, 0, 5, 8〉, v3 = 〈8, 1, 5, 6〉 and W a subspace of R4 spanned…

A:

Q: et aj = (1,3, –2), a2 = (5,1, 4), and b = (6, –9,3). a) Project b onto the line through aj. b)…

A:

Q: te the above linear system (of one equation) as a homogeneous matrix problem.

A:

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

A:

Q: 1s) La L : A → R be the limsir operator Lip(z)) – p(0)r*+27/(c). Find the matrix A representing with…

A:

Q: Let R2x2 be a linear space with all 2 × 2 real matrices. (1) Find a basis of R22 and dim (R²x2); (2)…

A: Given  be a linear space with all  real matrices.Therefore .We need to find the basis of .The inner…

Q: Prove det(A) = det(A'), for an upper triangular matrix A.

A:

Q: Let A be a 9x6 matrix with nullify equal to 1 a) find the rank and nullify of A^T  b) suppose that…

A:

Q: 4. (a) Let {b,, b2, b3, bą} be an orthonormal basis for a three-dimensional subspace of Rº, and let…

A: For (a), Note that {b1, b2, b3, b4 } be an orthonormal basis. We are given that u = b1-2b2+b3-2b4…