Problems
For Problems 1-5, determine whether the given set of
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Differential Equations and Linear Algebra (4th Edition)
- 2. If , and the vector is drawn with its tail at the point, find the coordinates of the point at the head of .arrow_forwardList a set of three vectors in R2 that spans R2 from which you can any remove any two of the vectors and still span R² with the remaining one vector. List a set of three vectors in R2 that spans R2 from which you can remove either of two particular vectors and still span R² with the remaining two vectors. However, if you remove the third vector, the remaining two vectors will not span R². State which vectors can and can't be removed. List a set of three vectors in R² that spans R² from which you can remove two particular vectors and still span R² with the remaining one vector. State which vectors can be removed. List a set of three vectors in R2 that spans R2 from which you cannot remove any one of the vectors and still span R2 with the remaining two vectors.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
- For each of the following lists of vectors in R3, determine whether the first vector can be expressed as a linear combination of the other two. (a) (-2,0,3) ,(1,3,0),(2,4,-1) (b) (1,2,-3) ,(-3,2,1) ,(2,-1,-1) (c) (3,4,1) ,(1,-2,1), (-2,-1,1) (d) (2,-1,0) , (1,2,-3), (1,-3,2) (e) (5,1,-5) , (1,-2,-3), (-2,3,-4) (f) (-2,2,2) ,(1,2,-1) ,(-3,-3,3)arrow_forwardProblem #7: Suppose that u, v, and w are vectors such that Problem #7: = 4, = -6, = 3, ||u|| = 1, ||v|| = 7, ||w|| = 8. Evaluate the following expression.arrow_forwardIf k is a real number, then the vectors (1, k), (k, k+ 56) are linearly independent precisely when k # a, b, where a = , 6 = and a < b.arrow_forward
- Solve the following two problems. You can use your calculator or MATLAB, but you will need to justify your argument and conclusions 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0,-1] in R. Decide whether they are linearly independent.arrow_forward[] for Ax=0? Let and 121 be be two solutions of Ax=0. Then which of the following vectors may NOT be a solutionarrow_forwardProblem 3 Decide whether is a linear combination of the vectors 3 If yes, find the coefficients. ------ աշ = = 9 V= -5 2 - 8 - and uz = 2 -2 1arrow_forward
- Problem 6 With the least amount of work possible, decide whether the following sets of vectors are linearly independent, and give a reason for each answer. (One or two senténces at most.) 000 a) { }arrow_forwardIn Problem ,use the vectors in the figure at the right to graph each of the following vectors. 3v + u - 2warrow_forwardConsider the following vectors à = 2ī + 3j and b = −2ī + 3k and c = −3ī + karrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning