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- Find the nullity of T, if a. T: R5 R2 and rank(T) = 3. b. T: P3 P4 and rank(T) = 2. c. T: M3x1M1×3 and rank(T) = 0. d. T R R and rank (T) = 1.arrow_forwardThis problem deals with the RL circuit shown here, a series circuit containing an inductor, a resistor, and a source of electromotive force (emf), but no capacitor. The linear first-order differential equation governing the current in this circuit is given by the following. LI' + RI = E(t) Suppose that L = 5 H, R = 202, and the source E of emf is an alternating-current generator that supplies a voltage of E(t) = 100 cos (40t) V. Suppose that the switch is initially in position 2, but is thrown to position 1 at time t = 0 so that I(0) = 0. Determine the subsequent inductor current, I(t). E Switch 2 R wwarrow_forwardI would like to get help to know how to make a report of the multiple regression analysis I performed about 30 employees salaries. it should include a description of the predictice model, pre-analysis, regression analysis, interpretation of the relevant findings and a conclusion with recommendations. thank youarrow_forward
- tion: Solve the following systems using Gaussian Elimination with Backward substitu- x- 2y+32=9 -x+3y =-4 2x-5y+5z = 17arrow_forwardProve the following inequalities: Ꮖ 1. x - x2 0 2 2. sin x > x - 3³ for x > 0 6arrow_forwarda. T: Show that following transformations are not linear. R3 → R³ T(x, y, z) = (x + y, 2, z − y) R² → R b. T: T(x, y) = x²yarrow_forward
- Given the characteristic polynomials p(x) for matrix Anxn find (a) n (size of A) and (b) its eigenvalues a. p(x) = (x − 1)²(x + 2)² (x − 4) b. p(x) = x² -5x+6arrow_forwarda. T: b. T: Find standard matrix of following linear transformations. R² → R² T(x,y)=(c,y+2x) R³ → R² T(x, y, z) = (x + y, y − z)arrow_forward26 5G II. 8:44 ☐ myportal.aum.edu.kw ENGLISH العربية RH Problem 2 [20 points]: Find the Reduced Row 1 4 7 Echelon Form of the matrix -1 0-1 3 04 Problem 3 [30 points]: Consider the following linear system: x+2y=1 -2x+2my=0 a) Write the linear system in the matrix form: A.X=b. b) For m=1, find the inverse of A, using the definition of the inverse. In this case, deduce the solution of the system. c) Use the definition of the inverse to find the values of m for which A is not invertible. 7 A▾ III G B I Ff▾ < ↑arrow_forward
- Calculate the determinant of following matrices 1 4 -2 a. A = 3 2 0 -1 4 3 -3 0 Ο b. B 7 11 0 1 2 2arrow_forwardhelparrow_forwardFind the future values of the ordinary annuities at the given annual rate r compounded as indicated. The payments are made to coincide with the periods of compounding. (Round your answer to the nearest cent.) PMT = $140, r = 4.5%, compounded weekly for 15 yearsarrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,