Consider the subspaces U = span{[1_5_3],[-4 3 -1]} W = span{[_4_2_-4],[-18_0−16]} 1x3. Find a matrix X E V such that U ~ W = span{X}. ]

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A: a) Suppose that    be  a  basis  of      Then, which is  a  contradiction.    Hence, is  not a…

Q: One of the following subsets of R² is not subspace. Select one: а. X1 S={ X1=2x2} b. S={ ,X1 =X2} C.…

A: We will check that which subset is not a subspace of R2

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A: Suppose that A is a m -by- n matrix that maps vectors in R^n to vectors in R^m. The four fundamental…

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

Q: Find a basis of the subspace ofRª defined by the equation 7x1+9x2+ 6x3 + 5x4 = 0. Basis:

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Q: 1. True/false: all linear functions U:M_(3x2)(F)->F^6 are isomorphisms. 2. True/False: If P and Q…

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Q: Linear Algebra: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a…

A: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2.

Q: Let ~v and ~w be column vectors in R^n, and let A be an n×n matrix. Prove that, if {A (~v), A (~w)}…

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Q: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W. Show that V ∩W…

A: Suppose V,W are subspaces of R^n. Let V ∩ W be all vectors which are in both V and W.  We have to…

Q: Let V be the subspace of P^4 spanned by B = {1,x^2,x^4}. Create a chnage of basis matrix Cd,b if D =…

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Q: Consider the subspaces U = span{[4 0 1],[4_1 −4]} W = span { [-5 3 3], [-5 3],[−5 4 −2]}

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

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

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Q: АT (Ь — Ах) — ӧ. Interpret this statement in terms of the fundamental subspaces of A.

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Q: True or False, S is a subspace of R 3 x1 (8] x2 x3 S = O True O False 2x1 + x3 = 0, x1 + x2 = x3 = 0…

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Q: Determine whether the given subset is subspace of R^3 W={(x1,x2,x3):x1+x2+x3=0}

A: Let the subset W is given as W={(x1,x2,x3)| x1+x2+x3=0} Determine whether the given subset is…

Q: Do vectors of the form {[ ]:x*+y*+z"<1} form a subspace of ie?? please explain what 37

A: The given set is                             xyz : x2+y2+z2≤1 Definition of Subspace: Let V be a…

Q: Given 7: -9 -10 0 find the closest point to in the subspace W spanned by -5 -6 -4 and 64

A: We have to find out the closest point of  in the subspace W spanned by Here noted that ,let,So…

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A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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Q: Find a basis for the following subspace of R°: W3D {(aj + 5а2 — 2а3, 2а1+ 6а2 — аз, Зај + 7а2) : ај,…

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Q: In linear algebra, a subspace of R^n can have a dimension less than n.  (True or False)

A: Given that the space and subspaces of the space. In general the subspace of every space have…