1. Consider the vectors a = (1,0, -2, 1), b = (0, 4, 4, 1), and c = mine the vector a-2b+2c. (5, 1, 1, 1) in R4. Deter- 2. Are the following sets vector space with standard addition and scalar multiplication? (a) V = {(x, y, z) : x² + y² + z² = 0} (b) V = {p(x) = P2: p is even that is p(x) = p(-x)} (c) V = {AЄ Mn,n; A is asymmetric that is A = -AT}

Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: 5.PT. PLN has $140000 to invest. The alternative investments and the corresponding annual returns…

A: According tot he given information it is required to form an linear programming problem for the…

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: Consider the vectors u₁ = ------- 2 and the vector : 3 B = If IS in the span of ₁, ₂, 3, 4, write…

A: The given vectors, and the vector .The aim is to find the coefficient of the linear combination of…

Q: Is every vector in R2 a linear combination of the vectors (1,-2) and (-2,1)? Provide a detailed…

A: Let (a,b) ∈ R2 , We write the (a,b) is the linear combination of the given vector (1,-2) and (-2,1)

Q: Write each vector as a linear combination of the vectors in S. (Use s, and s2, respectively, for the…

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Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

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Q: Show that the vectors are orthogonal.

A: Given vectors are u=<u1, u2>=<4, -1>v=<v1, v2>=<2, 8>

Q: Suppose that v1 = (5, 2, 0, 3), v2 = (2, -2, 8, 2) and v3 = (-6, 0, 5, 4). Is the following vector…

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Q: Suppose that v1 = (5, 1, 0, 5), v2 = (5, -3, 6, 2) and v3 = (-5,0, 5, 2). %3! Is the following…

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Q: a) Use the dot product to verify the type of angle connecting the vectors and y (acute, right or…

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Q: Find a vector orthogonal to all vectors in the set ((2,1,2), (2, – 2,3)) . Write your answer as an…

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Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

A: We have to prove that the given Column vectors are linearly dependent in R4.

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: Suppose and are vectors such that a × b =(3, 1, 4). What is the cross product of twice of a with…

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Q: lowing vector in the span{V₁, V₂, V3}? 8,9) me vector is in the span. me vector is not in the span.

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Q: Suppose that v1 = (4, 1, 0, 4), v2 = (2, -4, 5, 2) and v3 = (-2, 0, 3, 6). Is the following vector…

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