Question

In: Advanced Math

determine the orthogonal bases for subspace of C^3 spanned by the given set of vectors. make...

determine the orthogonal bases for subspace of C^3 spanned by the given set of vectors. make sure that you use the appropriate inner product of C^3

A=[(1+i,i,2-i),(1+2i,1-i,i)

Solutions

Expert Solution


Related Solutions

2a. Find the orthogonal projection of [9,40,-29,4] onto the subspace of R4 spanned by [1,6,5,6] and...
2a. Find the orthogonal projection of [9,40,-29,4] onto the subspace of R4 spanned by [1,6,5,6] and [5,1,5,5]. Answer choices: [2,14,-15,7] [-32,13,-10,7] [0,9,12,6] [-5,-2,3,2] [-12,0,-9,-9] [-16,20,0,4] [27,29,29,21] [-3,1,2,7] [-23,7,-3,-9] [-15,5,-15,30] 2b. Find the orthogonal projection of [17,18,-10,24] onto the subspace of R4 spanned by [2,7,1,6] and [3,7,3,4]. Answer choices: [-34,-22,-29,-34] [-6,4,-2,0] [-12,36,21,33] [3,21,-3,24] [7,-14,-12,1] [5,3,32,45] [14,32,12,11] [9,13,18,11] [20,2,-3,19] [-2,-6,1,-7]
Using least squares, find the orthogonal projection of u onto the subspace of R4 spanned by...
Using least squares, find the orthogonal projection of u onto the subspace of R4 spanned by the vectors v1, v2, and v3, where u  =  (6, 3, 9, 6), v1  =  (2, 1, 1, 1), v2  =  (1, 0, 1 ,1), v3  =  (-2, -1, 0, -1).
Is the given set of vectors a vector subspace (Give reasons)? If your answer is yes,...
Is the given set of vectors a vector subspace (Give reasons)? If your answer is yes, determine the dimension and find a basis. All vectors in R5 with v1 + 3v2 - v3 = 0, 3v1 + v2 - v4 = 0, 4v1 + 2v2 - v5 = 0 (v1, v2, … denote components). Show details.
Determine whether the given vectors are orthogonal, parallel, or neither. 32. (a) u = (-5, 4,...
Determine whether the given vectors are orthogonal, parallel, or neither. 32. (a) u = (-5, 4, -2), v = (3, 4, -1) (b) u = 9i-6j+3k, v = -6i+4j-2k (c) u = (c, c, c), v = (c, 0, -c)
Determine if each of the following sets of vectors U is a subspace of the specified...
Determine if each of the following sets of vectors U is a subspace of the specified vector space, and if so, describe the set geometrically: (a) U ⊆ R2, where U = {〈x1,x2〉 : x1 = 0} (b) U ⊆ R2, where U = {〈x1,x2〉 : x1x2 = 0} (c) U⊆R3,whereU={〈x1,x2,x3〉:〈1,2,3〉·〈x1,x2,x3〉=0} (d) U ⊆ R3, where U = {〈x1,x2,x3〉 : 〈1,2,2〉 · 〈x1,x2,x3〉 = 0 and 〈1, 3, 0〉 · 〈x1, x2, x3〉 = 0}
Define a subspace of a vector space V . Take the set of vectors in Rn...
Define a subspace of a vector space V . Take the set of vectors in Rn such that th coordinates add up to 0. I that a subspace. What about the set whose coordinates add up to 1. Explain your answers.
Determine whether the members of the given set of vectors are linearly independent. If they are...
Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them of the form c1x(1) + c2x(2) + c3x(3) = 0. (Give c1, c2, and c3 as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) x(1) = 9 1 0 , x(2) = 0 1 0 , x(3) = −1 9 0
Use the Gram-Schmidt process to construct an orthogonal basis of the subspace of V = C...
Use the Gram-Schmidt process to construct an orthogonal basis of the subspace of V = C ∞[0, 1] spanned by f(x) = 1, g(x) = x, and h(x) = e x where V has the inner product defined by < f, g >= R 1 0 f(x)g(x)dx.
There are three vectors in R4 that are linearly independent but not orthogonal: u = (3,...
There are three vectors in R4 that are linearly independent but not orthogonal: u = (3, -1, 2, 4), v = (-2, 7, 3, 1), and w = (-3, 2, 4, 11). Let W = span {u, v, w}. In addition, vector b = (2, 1, 5, 4) is not in the span of the vectors. Compute the orthogonal projection bˆ of b onto the subspace W in two ways: (1) using the basis {u, v, w} for W, and...
In parts a, b, and c, determine if the vectors form a basis for the given...
In parts a, b, and c, determine if the vectors form a basis for the given vector space. Show all algebraic steps to explain your answer. a. < 1, 2, 3 > , < -2, 1, 4 > for R^3 b. < 1, 0, 1 > , < 0, 1, 1> , < 2, 0, 1 > for R^3 c. x + 1, x^2 + 1, x^2 + x + 1 for P2 (R).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT