Find a basis for the subspace of R4 spanned by (1,0,-2,1), (2,-1,2,1), (1,1,1,1), (0,1,0,1), (0,1,1,0) containing...

Find a basis for the subspace of R4 spanned by (1,0,-2,1), (2,-1,2,1), (1,1,1,1), (0,1,0,1), (0,1,1,0) containing the first and fifth vectors

Expert Solution

Colby Messinger answered 2 years ago

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).

Find all the vectors in R4 that are perpendicular to the three vectors <1,1,1,1>, <1,2,3,4>, and...

Find all the vectors in R4 that are perpendicular to the three vectors <1,1,1,1>, <1,2,3,4>, and <1,9,9,7>

Find a basis for R4 that contains the vectors X = (1, 2, 0, 3)⊤ and...

Find a basis for R4 that contains the vectors X = (1, 2, 0, 3)⊤ and ⊤ Y =(1,−3,5,10)T.

consider the subspace W=span[(4,-2,1)^T,(2,0,3)^T,(2,-4,-7)^T] Find A) basis of W B) Dimension of W C) is vector...

consider the subspace W=span[(4,-2,1)^T,(2,0,3)^T,(2,-4,-7)^T] Find A) basis of W B) Dimension of W C) is vector v=[0,-2,-5]^T contained in W? if yes espress as linear combantion

1. Consider the following game: L R L 2,1 0,0 R 1,0 3,2 a)Find all Nash...

1. Consider the following game: L R L 2,1 0,0 R 1,0 3,2 a)Find all Nash equilibria and derive the players’ expected payoffs in each of the Nash equilibria. b)Now change the payoffs slightly so that L R L 2,1 2,0 R 1,0 3,2 i.Derive all Nash equilibria for this modified game. ii.Have any of the Nash equilibria changed? If so, for each player explain why the player has or has not changed her strategy. c) Do the players in...

Find a basis for the subspace of Pn defined by V={p an element of Pn, such...

Find a basis for the subspace of Pn defined by V={p an element of Pn, such that p(1)=0}. What is the dimension of V?

(6) In each part below, find a basis for R4 CONTAINED IN the given set, or...

(6) In each part below, find a basis for R4 CONTAINED IN the given set, or explain why that is not possible: Do not use dimension (a) {(1,1,0,0),(1,0,1,0),(0,1,1,0)} (b) {(1,−1,0,0),(1,0,−1,0),(0,1,−1,0),(0,0,0,1)} (c) {(1,1,0,0),(1,−1,0,0),(0,1,−1,0),(0,0,1,−1)} (d) {(1,1,1,1),(1,2,3,4),(1,4,9,16),(1,8,27,64),(1,16,81,256)}

(5) In each part below, find a basis for R4 that contains the given set, or...

(5) In each part below, find a basis for R4 that contains the given set, or explain why that is not possible: (a) {(1,1,0,0),(1,0,1,0),(0,1,1,0)} (b) {(1,−1,0,0),(1,0,−1,0),(0,1,−1,0)} (c) {(1,1,0,0),(1,−1,0,0),(0,1,−1,0),(0,0,1,−1)} (d) {(1,1,1,1),(1,2,3,4),(1,4,9,16),(1,8,27,64),(1,16,81,256)}

Find a basis and the dimension of the subspace: V = {(x1, x2, x3, x4)| 2x1...

Find a basis and the dimension of the subspace: V = {(x1, x2, x3, x4)| 2x1 = x2 + x3, x2 − 2x4 = 0}

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