6. Let Vi and V2 be subspaces of R" such that Vi C V2. Show that any vector v E R" can be uniquely written as v = a +b+ c with a e Vi, b e Vn V2, and c e V-.

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: 2. Using the definition of linear dependence prove that any set of vectors containing the zero…

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Q: and ā is a cC 7) will be

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Q: In order for vectors and t- 3 in a vector space R3 to be linearly t+4 in depen den t what should t…

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Q: - c(13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18) Fine the vector y by the…

A: year x 1951 13 1952 23 1953 21 1954 27 1955 37 1956 52 1957 34 1958 42 1959 31…

Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

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Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: 7.) for which value(s) of k are the following vectors linearly independent? u =

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Q: Q3\Find each the following: (1 2 3 4) 3. Order of (2 3)(6789). (A) (B) (C) (D) (246 8). Order of (1…

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Q: {(1, 2, 3),(3, 2, 1),(0, 0, 1)}. Show that B is linearly independent and spans R3.

A: Linear span: Let V represent a vector space, and S=(v1,v2,...,vn) represent a subset of V. If every…

Q: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

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Q: Determine the real value/s of c such that the following vectors are linearly independent: 4 - 2 -6 6…

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Q: 18 as a linear combination of a and y Express the vector v y.

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Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

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Q: Prove that the set of vectors of the form (a, b, c) where b = a +c is a subspace of R³.

A: According to the given information, it is required to prove that:

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: }] respectively. Let y = and u = . Write y as the sum of two orthogonal vectors, y, in the span of…

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Q: 5а+ 2b Decide whether the set of all vectors of the form is a subspace of R³ or a

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Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

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: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: Let u = (2, −1, −1) and v = (5, -3, 3). A vector with integer components perpendicular to ū and v is…

A: <-6, -11, -1>Explanation:Step 1: Determine how to find the perpendicular vector To find a…

Q: 5 Suppose that u = 1 2 and v= 0 are vectors in R³. Determine the smallest 2 --- 2 subspace H of R³…

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

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Q: . The distance of a point in the 3-D system from the origin a. is defined by the absolute value of…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

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