(a) Check whether the vector (3,-1, 4) can be expressed as a linear combination of u = (1, -1,0), v = (0,1,1) and w = (3,-5,-2) (b) Determine which subsets below are subspaces of given V. 1) V = R, W = {(x, y, z) | x+ 2y 3z = 4} 2) V = M, (R), W= subset of non-singular matrices

Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Find a subset ofbthebvectors v1=(0,2,2,4), v2=(1,0,−1,−3), v3=(2,3,1,1) and v4=(−2,1,3,2)that forms…

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Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: Let W be the subspace spanned by the vectors (1,2, 0, 3) and (2, 1,3,0). Find : a basis for W+.

A: Given that W is a subspace spanned by the vectors 1 , 2 , 0 , 3 and 2 , 1 , 3 , 0 . i.e., W = span1…

Q: False/True: If vectors V1, V2, ..., Un span the subspace V, then every vector in V can be written as…

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Q: Which one of the followings is NOT the subspace of R2 ? W = {(0,–2a): a e R} - W = {(2a, a): a e R}…

A: To find which one is not a subspace.

Q: Find the dimension of the subspace spanned by the given vectors: u₁ = (1, 3, -2,5), u₂ = (0, 1,-1,…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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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: Let W be the subspace spanned by the u's. Write y as the sum of a vector in W and a vector…

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Q: Find the terminal point Q of the vector v = 7i-j+3k given the initial point is P(-2, 3, 5) О (5, 2,…

A: In this question we have to find the terminal point of Q.

Q: Can you provide a sketch or model of the vector function (x,y,1-(x+y)) and show it passing through…

A: The sketch can be plotted using 3D modelling tools. In the modelling tool, select the appropriate…

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: Consider the three vectors V1 = (1,0,0, –1), v2 = (0, 1, 1, 0), V3 = (1, 1, 1, 1). Let W be the…

A: Given that W be a subspace of R4 spanned by the vectors. v1=(1,0,0,-1), v2=(0,1,1,0), v3=(1,1,1,1)…

Q: Let U1, U2, U3 – be the following subspaces of R4   U1={a, b, c, d) R4| 1b=с; a=d=0};   U2={(a, b,…

A: The given subspaces of ℝ4 are U1={a, b, c, d) ℝ4| 1b=с; a=d=0};   U2={(a, b, c, d)  ℝ4| a - b + 2c +…

Q: ()-(G) *-() --() 2. Which set of vectors below are linearly independent: V,= Select one: O A. none…

A: We have to find which set of vectors are linearly independent.…

Q: 8. Let W denote the subspace of R5 consisting of all the vectors having coordinates that sum to…

A: Consider the provided question,Write the given vectors into a matrix as below,

Q: b) u = (3, -1), v = (1, 5) et w = (8, -2) c) i = (1, 0, 0), j = (0, 1, 0) et k = (0, 0, 1) gajte…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

Q: Given any linearly independent set of vectors V = {v, V2, , }, prove that there is at least one…

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Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: 2. Consider the vectors v₁ = [1, 1, 1] and v2 = [1, 0, 0]. These two vectors define a 2-dimensional…

A: Let us find the projections.

Q: →→→ Let x, y, z be vectors such that x X X y x z →→ = a; y x ➜>> Z X X y = b and ° {(+5) x = -(-+)}…

A: It is given that x→=y→=z→=2 x→,y→,z→  makes angle of 600 with each other.x→×y→×z→=a →  ; y→×z→×x→=b→…

Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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Q: What are the possible values of b that make (25x? + bxy + 81y²) a perfect square trinomial? Explain…

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Q: Let v1=[-2,2,1], v2=[-8,7,4], v3=[-29,25,14], w=[6,6,1] is W in {v1,v2,v3}? how many vectors are…

A: a) Given that v1=-2,2,1,v2=-8,7,4,v3=-29,25,14,w=6,6,1. It is required to find whether w is in…

Q: There are four vectors (1,a,b,c), (1,1,1,1), (1,2,3,1), (3,4,5,3). If the vector space (subspace)…

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