PROBLEMS
For Problems 1-14, determine the component
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Chapter 4 Solutions
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- 1. Let (1,2) and 7: = (a) For which value of a the two vectors an are parallel? For which value of a they are orthogonal to each other? (b) For which value(s) of a the two vectors an 2. Consider the vectors (a) Is (b) Is = (3, a) be two vectors in R². Let = (1, 1, 1, 1) (1,2,3,0), = (0,1,2,3) and = (2,3,4,-3) a linear combination of a linear combination of are linearly independent? and ?? , and ?arrow_forward1. Let x = i +4j + 2k and y = i-3j - k. In this question, write all vectors in i, j, k notation. (a) ( Find |x||. (b) M Find 2x + 3y. (c) Find x. y. (d) Find x × y. Answer: Answer: Answer:arrow_forwardProblem #2: Let p = Problem #2: P₁ = 2x² + 6x + 9. Find the coordinate vector of p relative to the following basis for P2, 1 + x, P3 = 1+x+x². = 1, P2 Enter the coordinates, separated with commas.arrow_forward
- Please explain and do all steps so that I can understand this question.arrow_forwarda, b, and c are vectors. Then the expression a×c+b×a is (a) Meaningless (b) A vector collinear with a (c) A vector orthogonal to aarrow_forwardIf v is any vector and n is any unit vector: (a) Show that v can be expressed as v = (v · â) Â+ĥ×(v x î) where the two terms represent components that are parallel and perpendicular to ôn, respectively. (b) Write the equation given above in (a) in index notation.arrow_forward
- 2.2 #1 please answer A B C and D The problems are in the picture.arrow_forward2. Given a = 5e2 and b = 2e₁ + €3, let C = ab. If the tensor C operates on another vector d = 7e₁ +2e2- €3: (a) Calculate the resulting vector. (b) Symbolically, how would the result be expressed in terms of b, d and a?arrow_forward1 (a) Write the following vectors as column vectors. i. 42₁-323 +2ẻ₂ — 2ẻ₁ € R³. ii. ₂ + ₁ - 52₂ € R².arrow_forward
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