(a) Solve the initial value problem 2" +2r' + r = 8(t - 2), z(0)=1, 2'0)...
Kindly do these asap and clearly. Thanks (b) Consider the initial value problem ܚܕ ܠ ܂ (0) Find (t), writing your answer as a single vector. 1 k 0 (c) Consider the matrix 0 k 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A-1 exist? iii. For what value(s) of k does the linear system Aõ= 7 have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue?...
0 1 (c) Consider the matrix0 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue? v. For any vector be R*, find the value(s) of k for which the linear system A7 = b has a unique solution.
Need this asap Thanks k 0 1 (c) Consider the matrix 0 k 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A- exist? iii. For what value(s) of k does the linear system Ai= have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue? v. For any vector 5 € R", find the value(s) of k for which the linear system Až = b has a unique...
(b) Consider the initial value problem -2 1 z7) = 3 Find ö(t), writing your answer as a single vector.
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector UI, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. c. Solve the original initial value problem. n(t)- 2(t)
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)- (1 point) Consider the initial value problem -51เซี. -4 มี(0)...
Solve the initial value problem for r as a vector function of t. dr Differential equation: of = -7t i-5t j - 3t k Initial condition: r(0) = 7i + 2+ 3k r(t) = (O i+();+ ( Ok
PDE questions. Please show all steps in detail. 2. Consider the initial-boundary value problem 0
(b) Let f 0, 1-R be a C2 function and let g, h: [0, 00)-R be C1. Consider the initial-boundary value problem kwr w(r, 0) f(a) w(0, t) g(t) w(1, t) h(t) for a function w: [0,1 x [0, 0)- R such that w, wn, and wa exist and are continuous. Show that the solution to this problem is unique, that is, if w1 and w2 [0, 1] x [0, 00)- R both satisfy these conditions, then w1 = w2....