Consider the vectors v1, v2, ..., Um in R". Is span (01,..., īm) necessarily a subspace of R" ? Justify your answer.

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: (a) A: va+v. (b) A: (av). (c) A: √ av.

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: be an Given f: R³ → R, explain the relation between the following sets: {(x, y, 2) E R³: f(x, y, z)…

A: we have an invertible transformation on  T:R3→R3  and a function f:R3→R.

Q: Find a vector of matching dimension that is not in the given span. span

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Q: (2) For every vector u and vector v in se A) True B False

A: Introduction: Vector is a quantity that has both magnitude and direction. Some mathematical…

Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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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: Find a vector with norm 3 that is orthogonal to both the vectors x = Vector: < 1 2 and y = -4

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Let u =[3, -1] and v = [0, 1] can you find the vector[h, k] that is not in Span{u,v}? either give an…

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Q: Q1. Consider the following vectors: -- () ---- () --C) 2 3 1 3 (a) Do the vectors i, u, w span R³?…

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Q: X b) Let T 10 Find the Kernel of T. Write down the range of T as a span of independent 5x vectors.…

A: Obtain Kernel of T as follows.

Q: 2 -7' Let j = and u .Write j as the sum of two orthogonal vectors, , in Span {u} and 2 orthogonal to…

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Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

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