Let A={1,2,3,4} and let R be the relation from A to A R={(1,1),(1,4),(2,1),(2,2),(2,3),(3,1),(3,4),(4,3)} Create thr diagraph and matrix Mr for the relation
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- Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.V = Span{(1, 2, 3), (1, 0, 2)} and W = Span {(0, 2, 1), (1, 1, 1)}. Find the relation between V and W.
- please shows all the work, thank you!b) Given A = {1,2,3,4} and B = {x,y,z}. Let R be the relation from A to B. R = {(1,y),(1,z), (3,y),(4,x),(4,z)} Determine the matrix of the relation and hence discuss the relationship between R and AX B c) From b) above, draw the arrow graph of R.Let the set A = {2, 3, 8, 12} and the relation R defined as the following R = { (2, 2), (2, 8), (2, 12), (3, 3), (3, 12), (8, 8), (12, 12)} A. Represent R with a matrix (considering the elements of the set A listed in the same order as above) B. Determine the properties of the relation R (reflexive, symmetric, antisymetric, transitive, and/ or equivalence). C. Which of the followings describes R? 1. R = {(a, b) | a divides b} 2. R = {(a, b) | a > b} 3. R = {(a, b) | a + b < 15
- Let P(1, 2, 0), Q(4,6,0), and R(6,14,0) be 3 points in 3-space. Find the dot product of PQ and PR please use proper notation and show work3. Given, A = { 1,2,3,4 }, B = { x,y,z } Let R be the following relation from A to B: R = { (1,y),(1,z)(3,y)(4,x),(4,2) } a. Determine the matrix of the relation b. Draw the arrow diagram of R c. Find the inverse relation of R-'of RLet A = {2, 4, 5}, and let R be the relation on A consisting of pairs of the form (a, b), where ab > 12, and both a and b are elements of A. List the pairs in R and then represent R using a matrix.
- (2) Let aj = (1,2, -1), a2 = (3,0, 1) and bị = (-1, 10, 7), b2 = (1, 2, 0) in R³. %3D (a) Is a, in Span(a,)? (b) Which of bị, b2 is in Span(a, a2)? (c) Write each b; in Span(a1, a2) as a linear combination of a1, a2.Each of J, K, L, M and N is a linear transformation from R2 to R². These functions are given as follows: Jx1, х2) %3D (Зхі — 5х2, —6х1 + 10x), K(x1, x2) = (-V3x2, 3x1), L(x1, x2) = (x2, –x1), M(x1, x2) = (Зх1 + 5х, бх1 — бх2), N(x1, x2) = (-v5x1, v5x2). (a) In each case, compute the determinant of the transformation. . det J= ,det K ,det L= ,det M= ,det NConsider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R={(?, 1); (?, 3); (?, 2); (?, 3); (?, 4); (?, 2)}.(i)Deduce the matrix of the complementary relation, ???, clearly outline and comment on your result.(ii) A relation T is defined on the set Y above from Y to Y as ? ={(1,1); (4,2); (1,3); (2,4); (2,1); (3,2); (3,3); (3,4); (1,2); (2,3); (4,4); (4,1)}, compute and analyze ????−1. (b) Given the functions f and g de defined by ?(?) =6?+57?−5, ? ≠57; ??? ?(?) = 2?2 − 3? + 4. Critically analyze and deduce the formula defining the (i) composition function gof (ii) inverse function ?−1(c)Apply the Runge-Kutta formula as a tool for solving and analyzing numerical differential equation, critically compute and analyze the numerical solution of ?′ = ?(?, ?) = 1 + ?2, y(0) = 0. Computing for the first step, with ℎ = 0.5