Find the orthogonal projection of v = - projy(v) = 11 3 1 1 မြန်မ -1 onto the subspace V of IR 3 spanned by| –2 203 and 0

Q: Find the orthogonal projection of - -1 1 12 2 || subspace W of R4 spanned by -1 1 1 = 0 7 0 1 1 " −1…

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Q: O Linear subspace L is given by the equations 2r1 + r2 + 3r3 - 14 = 0 = 0 3r1 + 2r2 – 2r4 3r1 + 12 +…

A: Let AX=0 213-1320-2319-1x1x2x3x4=000R2→R2-32R1 , R3→R3-32R1…

Q: Find a basis for the indicated subspace of R³. The line of intersection of the planes with equations…

A: Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if  (i) S…

Q: Explain why, no matter how the circuit is completed, Pip must place an even number of additional…

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Q: Find the closest point to y in the subspace W spanned by V₁ and V₂ 2 2 - 1 y= a. 3/6 -2/6 丽··· -1/6…

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Q: Find an orthogonal basis for the subspace Span (1, 1 + x, 1 + x²) ≤ P3. Justify your answer!

A: Using the Gram Schmidt orthogonalisation process:

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (v) = - C 12 = 0 2 0

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Q: Determine whether W is a subspace of V

A: Given

Q: Find the orthogonal complement S⊥ of the subspace S of R3 spanned by the two column vectors of the…

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Q: Let u = (18,1,0). Find the orthogonal projection of u onto the subspace W spanned by the…

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Q: 13 Find the orthogonal projection of v = 7 onto the subspace V of R3 spanned by projy(v) = -12 1 -2…

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Q: Consider the subspace spanned by A ---- and 7₂ and the vector = basis {1, ₂}. = 5 9 in this…

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Q: Find the orthogonal projection of 0 0 -9 0 onto the subspace V of Rª spanned by -1 -1 -1 proj, (v) =…

A: Let V be the vector space spanned by v1,v2,v3,.....vn. The projection of v onto V is obtained as,…

Q: Let B Let v = x1 || 2 {]-G]} 3 13 15 then 8 0 be a basis for the subspace H. X1 where " x2 X2

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Q: Determine the dimension of the subspace of R consisting of all XeR* such that x1 + 2x, = 0 and X3 –…

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Q: Let W be the subspace of R³ spanned by the vectors Find the matrix A of the orthogonal projection…

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Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

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: True/False: If V is a subspace of R", then dim(V) + dim(V+) = n. True False

A: This is true and follows from a famous theorem in linear algebra.

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (7) 0 -8 v= 0 0·00 ||

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Q: Find the dimension of the subspace of all vectors in R° whose second and fourth entries are equal.…

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Q: (11) Find a basis for the orthogonal complement of the subspace of R" spanned by the vectors V1 =…

A: We have to solve given problem;

Q: (a) Determine whether the set of all vectors of the form (a,b,c), where b= a+c, is a subspace of R³.…

A: Consider the subset S of ℝ3 defined as, S=(a,b,c)∈ℝ3 | b=a+c Take  a1,a2,a3,b1,b2,b3…

Q: Find the orthogonal projection of v = projy(v) = [8] -25 H -7 onto the subspace V of R³ spanned by…

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Q: Find the subspace generated by the vectors A= (2,1,-5), B= (4,3,7) %3D %3D So in space R³

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw(7) = = -15] -8 v = -16…

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Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw (v) = 16 -20 -6 = 16 9…

A: We have to find the orthogonal projection of onto the subspace W of R4 spanned by Let v1 = and v2 =…

Q: 2 Find bases and dimensions for the four subspaces associated with A and B: A = 1 2 4 and B= = 1 24…

A: We will find the bases and dimensions.

Q: Find a basis for the subspace of R4 determined by the equation 2x-3y+4z w = 0

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Q: Find the orthogonal projection of 0 0 onto the subspace V of R¹ spanned by -1 1 1 -1 -1 -1 -1 -9 0…

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