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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_forwardProblem #4: Let p = 7x² + 3x + 4. Find the coordinate vector of p relative to the following basis for P2, P₁ 1, P2 = 1 + x, P3 1+x+x². =arrow_forwardI would need some help with problem #46 to find the vectors T, N, and B at the given point, please?arrow_forward
- 3. If a = 3x - 5ỹ and b = -2x +9y, write the vector 5a-86 in terms of x and yarrow_forwardDefine and x as the vectors y and x= [0.5, 1, 1.5, 2, 2.5] y=[0.8, 1.6, 2.4, 3.2, 4.0]. Then use them in the following expressions to calculate z using element-by-element calculations. (a) z = x² + 2xy 3 4 (b) z=xye*- xy +8.5arrow_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_forward
- Problem 6. Suppose that V₁, V2 and v3 are linearly independent vectors in a vector space V. Prove that the vectors W₁ = V₁ + V2, W2 = V₂ + V3 and w3 = V3 + V₁ are also linearly independent in V.arrow_forwardProblem 3: Write the vector u= 2 as a linear combination of the basis vectors 3 [- 27 - 3] V = 2, V = , and V, = 1 7 3 2.arrow_forwardFind the angle between the vectors [ 1 ] And [ -3 ][ 3 ] [ 2 ][ 2 ] [ 5 ]arrow_forward
- [1 1 1 -1 Let u1 = u2 Uz = then write x as sum of two vectors -3 3 on in span {u} and other one in span {u2, U3,} -2 2 x = 3 -3 (a) X = (b) 3 2 0. 3 [1 (d) 1 X = 3 -3 4. + +arrow_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_forwardFind the coordinate vector [x] of x relative to the given basis B = {b₁, D₂, D3}. b₁ = 1 -1 -4 b₂ = [x] = (Simplify your answer.) -2 3, b₂ = 8 2 -2 6 X = 5 -4 22arrow_forward
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