-9 4 -3 -21 Find the vector in the subspace W spanned by which is closest to –1 -3 -5 Answer:

Q: Given v: find the closest point 7 -6 to v in the subspace W spanned by and -4 1 -2 -18

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Q: 7 4 -7 find the closest point to v in the subspace W spanned by 2 and 4 -2 Given i -32

A: The given problem is to find the closest point to vector v in the subspace W spanned by given…

Q: The set of all polynomials of the form ax³ bx² cx + 2, where a,b and can real numbers is a subspace…

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Q: Given: a = [1 1 0 -1] b = [ 0 1 2 1] c = [ 1 0 1 -1] d = [ 1 1 -6 -3] e= [ -1 -5 1 0] Suppose, x =…

A: The basis is a set of linearly independent vectors that spans the given vector space. A basis is to…

Q: Find a linearly independent set of vectors that spans the same subspace of R³ as that spanned by the…

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Q: -6464 13. Find a basis for the subspace spanned by the vectors What is the dimension of the…

A: Solving

Q: -5 5. 10 8. Let A= 4 -7 -11, and define W = {C E M2x3 CA = 02x3}- %3D %3D -2 7. a. Prove that W is a…

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Q: -5 63 Given v -42 98 find the coordinates for v in the subspace W spanned by 4 3 3 -15 U2 and uz 1…

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Q: -5 -4 -2 and -6 -5 , find the closest point to v in the subspace W spanned by 8 Given v = -2 -6 -8…

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Q: -5 6 Given v = 1 -8 find the coordinates for v in the subspace W spanned by -7 -4 2 3 -2 1 5 and u4…

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Q: -2 3 Find the vector in the subspace W spanned by which is 1 27 closest to L 20] Answer:

A: *As this problem is related to Projection matrix, hope you know how to find inverse of a matrix,…

Q: Soal 1. 35. Find the closest point to y = (3,-1, 1, 11) in the subspace W spanned by V₁ = (1,-1,-1,…

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Q: -5 Given v 9 -3 find the coordinates for v in the subspace W spanned by

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Q: 2 -1 3 -1 -3 -2 -1 -6 -7 2 4 -8 6. Find bases and dimensions for the four subspaces associated with…

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Q: 3 1 Show that the null space of A is a 02 subspace of R³. Which subspace can you obtain by the…

A: It is given that,  A = 13-1024 We have to show that the null space of A is a subspace of ℝ3 and to…

Q: 5. The solution set of the system Ax 0 with three unknowns is a subspace of the vector space M33 O…

A:

Q: 6. (a) Determine whether the set of all vectors of the form (a,b,c), where b a+c, is a subspace of…

A: The subspace of R3 is (a,b,c) where b=a+c

Q: Find the dimension of the subspace spanned by the given vectors. - 1 - 7 4 3 2 - 1 - 10 7 ... The…

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Q: (a) Find all solutions to Ax = b with 3 2 9 7; b -3 3 4 3 A = 2 6. (b) What can be said about the…

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Q: 4. The two parts of this question are unrelated. (a) Consider the set of matrices of the form where…

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Q: 3 5 2 and find the closest point to i in the subspace W spanned by -5 Given i -6 3

A: Givenv→=34-55and let s1→=52-61 and s2→=0734The formula of orthogonal projection of v onto span of s1…

Q: -3 Find the orthogonal projection ŷ of y = -1 onto the subspace -2 5 W = Span { u1 = -5 u2 = -3 Ex:…

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Q: -11 -3 1 2 Find the orthogonal projection of v = onto the subspace W spanned by 43 -5 -3 3 4 5 projw…

A: Given: v→=-11243-3 and W is a subspace spanned by -32-53, -3254, 12-35.

Q: 1 3 6. 3 Let vị U2 = 1 U3 = 1 and w = | 2 2 Is w in the subspace spanned by{v1, v2 , V3}? Why ? Yes,…

A: Given v1 = 10-2v2 = 311v3 = 612w = 321 The equation x1v1+x2v2+x3v3=w will have a solution if the…

Q: -7 7 Given v = 7 -10 find the coordinates for v in the subspace W spanned by 1 -7 -4 -1 2 3 -2 1 U2…

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Q: 1 -2 14 Let v, = Determine if u is in the subspace of R* generated by (v1,V2.V3}. -8 V2 V3 7 and u =…

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Q: 7. The vector i = is in a subspace II with hasis B- 32 Find the B-coordinate vector of

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Q: 2 7 -6 find the closest point to v in the subspace W spanned by -4 9. Given v = -2 and 2 -9 -18

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Q: 4. Find bases and dimensions of the fundamental subspaces associated with the matrix 1 2 1 3 A = 4 2…

A: The pivot rows of a matrix A form a basis for A  . here A=12132426-213-6for  echelon form,…

Q: -2 -4 find the closest point to v in the subspace W spanned by -2 and 6 Given v = 7 70

A: To find  The closest point to V in the subspace W spanned by the given vectors.

Q: Find the orthogonal projection of -19 5 -5 -12 onto the subspace W of IRª spanned by 1 -4 and 5 10

A: As per the orthogonal Decomposition  theorem  Let us assume W is a subspace of Rn then each y in Rn…

Q: -7 7 Given v = 7 -10 find the coordinates for v in the subspace W spanned by -7 -4 -1 2 3 -2 U1 1 Uz…

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Q: Find the dimension of the subspace spanned by the given vectors. 2 5 4 9 24 - 19 The dimension of…

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Q: -5 -2 -4 Given v = find the closest point to v in the subspace W spanned by -2 and 7 70

A: Let consider  v=−19−2−3, u1=−5−26−1, u2=−4−4770

Q: - 2 -1 -5 2 1 - 9 3. Let T= 2 -8 - 2 1 Prove that span - 2 1 and | | 3 11 5 -5 -13 -7 | 3 span 1 - 4…

A: Let us consider a finite dimension vector space V over the field F. Define a linear transformation…

Q: Consider a subspace and a vector (:) (3) 1 H = Span- 2 X = %3D 2 7 Determine if x e H. If so find…

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Q: 1 -1 -2 1 1 1 1 2 { -1 1 -2 2 -1 } 1 1 1 1 -1 2 -2 1 The dimension of the subspace spanned by the…

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Q: -{() Show that W = :71 + 22 + x3 = 0} is a subspace of R3. Hint : Re- 3. I3 member, it's not enough…

A: According to the given information, It is required to show that W is a subspace of R3.

Q: 2. (a) Write one of the four vectors 3. 8. as a linear combination of some or all of the others. (b)…

A: a

Q: a 6. Let H be a subspace of M2x2 whose vectors are of the form Then, B 2 is a basis for H. 7 Find…

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Q: 1 4 Let 3= {b1, b} be a basis of a subspace H or R3, where b, = 5 1. b, = -7 If x = 4 is a vector in…

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Q: 1 -2 -3 Let v, ,V2 - 7 and w -3 Determine if w is in the subspace of R generated by v, and v2. -6 11…

A: To determine  If W is in tg subspace of R^3 generated by v1 and v2.

Q: 3. (a) Write one of the four vectors ü =| 1 2 3, = as a linear combination of some or all of the…

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Q: Consider the subspaces U = span{[3 5 0],[0 12 -6]} and W = span{[–3 2 -1],[-15 7 -11]} of V = RIX3.…

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Q: -15] 1 [2] Find the orthogonal projection of v: -11 onto the subspace V of IR spanned by and 0 -2…

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Q: 1 3 6. (4) (a) Find orthonormal vectors ĝ1, 2 in the subspace Span{a, b} spanned by ä = 7 of R5. 1…

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Q: The set W = : 3x - y = z - 5w = 0 %3D is a subspace of RT. What is the dimension of W Select one: а.…

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Q: -1-日 5 Let S be the subspace of R° spanned by the vectors and 2 2 . Find the matrix P for the…

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems.

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.