Find the distance from the vector -1 y = -5 10 to the subspace W spanned by -2 1 u 0 and v= 2 ||

Q: Express the vector == 7= Z+ y. -22] 10 as a linear combination of = -(-3) and y=

A: Consider the vector v→=-2210. To express it as linear combination of vectors x→=-4-5 and y→=1-5.…

Q: Find each of the following Given: u = ; v = ; w = 1. u.v 2. (u.v)w 3. u.(2v)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: H = 1 -3 2 -4 Determine the dimension of the subspace H, where 7 9 -6 12 2 -1 4 2 5 - -3 7

A: We know that the dimension of the vector space is the number of linearly independent vectors in the…

Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

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Q: Find the length of the vector x=x= |x|=|x|=

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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: Express the vector 12 x+ÿ. = [15] as a linear combination of a = 2 1 and y= -17 -2

A: Given

Q: The vector x is in a subspace H with a basis ß = {b₁,b₂}. Find the ß-coordinate vector of x. b₁ =…

A: The given basis is b1,b2=1-2, -53. To Find: beta coordinate vector of x=19-17 w.r.t the above basis.

Q: 3. Let W C R be an inner product subspace with standard dot product. { 12 then If W I1- 2r2 + 4 = I3…

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Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: 21 Find a basis for the subspace of R³ consisting of all vectors 2 such that -81 + 9x2 + 4x3 = 0 13…

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Q: H is the set of all vectors x = X2 in R³ with the property that X3 X1 + x2 = 0 and Xi – x2 + x3 = 0.…

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Q: Use the function to find the image of v and the preimage of w. T(V₁, V2, V3) = (4V2 V₁, 4v₁ + 5v₂),…

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Q: Find the vector equation for the line of intersection of the planes 5x + 3y2z = -1 and 5x + 5z = -4…

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Q: V {(x1 , X2, X3 ) E R³ |x2 + x3 = 3} %3D nin R3'ün bir alt uzayı olup olmadığını gösteriniz.

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Q: Let S = {[" e Mzxzi a = d and b + c = 0} be a subspace of M2x2- Then the dimension of S is equal to:…

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Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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