Concept explainers
True or False? In Exercises 83–86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
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Chapter 15 Solutions
Calculus
- Review Exercises Solving a Vector Equation In Exercises 5-8, solve for x where u=(1,1,2), v=(0,2,3) and w=(0,1,1) 3x+2uv+2w=0arrow_forwardTrue or false? In Exercises 43and 44, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) The orthogonal complement of Rn is empty set. (b) If each vector vRn can be uniquely written as a sum of a vector s1 from S1 and a vector s2 from S2, then Rn is direct sum of S1 and S2.arrow_forwardTrue or False? In Exercises 57and 58, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) To subtract two vectors in Rn, subtract their corresponding components. (b) The zero vector 0 in Rn is the additive inverse of a vector.arrow_forward
- True or False? In Exercises 79 and 80, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows that the statement is not true in all cases or cite an appropriate statement from the text. a If dim(V)=n, then any set of n+1 vectors in V must be linearly dependent. b If dim(V)=n, then any set of n1 vectors in V must be linearly independent.arrow_forwardTrue or False? In Exercises 57and 58, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) Two vectors in Rn are equal if and only if their corresponding components are equal. (b) The vector v is the additive identity of v.arrow_forwardTrue or False? In Exercises 9598, determine whether the statement is true or false. Justify your answer. If u is a unit vector in the direction of v, then v=vu.arrow_forward
- Orthogonal Vectors In Exercises 77 and 78, let v=(v1,v2) be a vector in 2. Show that (v2,v1) is orthogonal to v and use this fact to find two unit vectors orthogonal to the given vectors. v=(12,5)arrow_forwardTrue or False?In Exercises 73 and 74, determine whether the each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a The length or norm of a vector is v=|v1+v2+v3++vn|. b The dot product of two vectors u and v is another vector represented by uv=(u1v1,u2v2,u3v3,,unvn).arrow_forward
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