In Exercises 1–6, determine which sets of
3.
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- In Exercises 11–14, find the value(s) of for which the vectors are linearly dependent. Justify each answer.arrow_forwardSection 5-2 : Vector Arithmetic 1. Given ā = 31 -9j and b = -6i +j compute each of the following. (a) 105 (b) 14ã + 205 (c) 8b – 3 2. Find a unit vector that points in the same direction as a = (10,-3,8,-2). 3. Find a unit vector that points in the opposite direction as č = 2i +7j - 5k . 4. Find a vector that points in the opposite direction as ā = (-3,–14,2) with a magnitude of 32. 5. Determine if i = (1,0,-4) and w= (9,3,1) are parallel vectors.arrow_forwardIn Exercises 11–14, find the value(s) of h for which the vectors are linearly dependent. Justify each answer.arrow_forward
- The following question is from linear algebra first year: Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step. Can we get integers as answers?arrow_forward6. Show that the vectors (1,1,0), (1, 0, 1), and (0, 1, 1) generate F³.arrow_forwardIn Exercises 26–34, use properties of determinants toevaluate the given determinant by inspection. Explainyour reasoning Please show all workarrow_forward
- 1. Find the sum of the vectors (3,-1) and (-1,5) and illustrate geometrically.arrow_forwardPart b L Let U₁ = 1 + x + 4x², U₂ = 2x + 5x², U3 = 2 + x + 7x². Determine whether these three vectors are linearly independent or not.arrow_forwardSolve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 2 1 -2 2 3 -4 1 1 1 - Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P- AP is a diagonal matrix D. Give Darrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage