1 -1 Find the distance from y to the subspace spanned by u. U= y= NO N1

Q: The set W : 3x - y = z -5w = 0} is a subspace of R*. What is the dimension of W Select one: а. 1 b.…

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Q: 1 -3 0 Let v¹ 3 1 ,w= -5 and determine if w is in the subspace of R³ -2 2 generated by v¹ and v².…

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Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y + 13 V₂ = 1 6 The closest…

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Q: 3. Let V1 and V2 be subspaces of R" (over R) Their intersection V=V,nV, is the set of 2 all vectors…

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Q: Find the projection of the vector v onto the subspace S. S = span projs v= 0 -1 11 O

A: We have to find the projection of the vector v onto the subspace SWhereS = span   and v = Let v1 =…

Q: u1 O Given a subset U of R² defined by U = |2u1 = u2 Show that U is U2 a subspace of R3

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Q: Q.4 Show that U {(x, -x) |x in R} is a subspace of R. %3D

A: To Prove U is a subspace of vector space V 1) 0∈U  If x, y∈U  and a∈V  2) Closed under vector…

Q: [5 Find the orthogonal projection ŷ of y = onto the subspace 3 W = Span { uį = 2 u2 3 Ex: 1.23 ŷ =

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Q: Find the projection of the vector v onto the subspace S. 0 0 1 0 1 0 S = span V = 1 1 -1 - 1 1 - -1…

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Q: Let the Euclidean space of 2x2 type matri with inner product defined by V, (A / B) = Isometry(B'A)…

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Q: 4. Determine whether W is a subspace of R³. a. W = {(x-1, x,x) x ER} b. W = {(3x, 0,-x)|x = R} 3 x 0…

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Q: 7. Let W be the subspace spanned by the u's, find the vector in the subspace W that is the closest…

A: The following is the MATHEMATICA CODE required to perform the operation specified in the given…

Q: 6t Let H be the set of all vectors of the form Find a vector v in R such that H = Span{v}. Why does…

A: Given that H be the set of all vectors of the form 6tt5t. Here, v=615. H=span615 Now, H forms a…

Q: Which of the following is a subspace of p2? O a. R2 x, e R W = Зх, + 1 1. Ob. W = ER| x*2 2 0 C. ER?…

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Q: Given v = U₁ = 0 find the coordinates for v in the subspace W spanned by 1 [3] 0 -1 V = -9 3.33 -3 7…

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Q: Find the orthogonal decomposition of v with respect to the subspace W. (That is, write v as w+u with…

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Q: Find the closest point to y in the subspace W spanned by v₁ y = 5 1 1 15 - 1 1 - -1 2 V2 - 3 1 0 2…

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Q: 4t + 2s 5s Question : Let H be the set of all vectors of the form Find 3t 2s – 3t two vector v, u E…

A: In the question it is provided that H is a set of all vectors of the form  4t+5s5s3t2s-3t The…

Q: Let v₁ = 1 and ₂ = 1 (a) x-z = 0. 1 The subspace spanned by v₁ and v₂ in R³ is a plane whose…

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Q: -8 -5 -1 6 -4 --- U₁ = -5 -6 -7 -10 1 -18 Compute the distance d from y to the subspace of R4…

A: Given: y=-8-1-5-10, u1=-56-61, u2=0-4-7-18To find: The distance, d from y to the subspace of ℝ4.

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.