Page 4 1 -110 (6.) [20 pts.) Solve the homogeneous linear system x' = pt, x(0)...
4. Solve the nonhomogeneous linear system of differential equations 2. Solve the nonhomogeneous linear system of anerential equations () u-9" (). 3. Solve the homogeneous linear system of differential equations 1 ( 2 ) uten ( 46 ) + ( ). 4. Solve the nonhomogeneous linear system of differential equations 43,742 cos(46) - 4 sin(40) (10 5 cos(40) ) +847, 7 4cos(46) + 2 sin(40) 5 sin(46) 5. Solve the initial value problem for the nonhomogeneous linear system of differential...
Solve the following first order linear non-homogeneous system using projection matrices: s x' = 2x – y + 1, x(0) = 0 ly' = 3x – 2y + 2, y(0) = 2 where x = x(t), y = y(t).
21 13 pts) 2. Find a basis for the solution space x of the following linear homogeneous system of equations: 1+2 +3 +14 213r2+4r3- 5x4 4x1+6r2 +8T3- 10x4 6r1 +9r2 +12r3 - 15r4= 0 0 Your solution must include verification that the basis spans the set of all solutions and is linearly independent. 21 13 pts) 2. Find a basis for the solution space x of the following linear homogeneous system of equations: 1+2 +3 +14 213r2+4r3- 5x4 4x1+6r2 +8T3-...
1. (8 pts.) Suppose T is a linear transformation and -(1)-(C). --- () - 0 Solve the matrix vector equations below. Explain 2. (8 pts.) Below are a matrix A, its inverse, and a vector b. 1983--013... (1) A = A-1 = 1-4 3 2 -5 7 2 0 1) , and b = x) Determine the value of x. Then solve the matrix vector equation Av = b. [-u-5 il 14 s1 3 70 | 71-3-70 12 x 12...
6. (15 pts) For the linear system 3x + 2y + 10x = -6 3 + 2z = y+2z = 3 3+ 4y + 10% = 8 a) Use your calculator to place the augmented matrix in RREF and write it here. 3 2 10 -6 i 470 - 4 3 8 b) Find the general solution to the linear system, written as either the vector equation of a line or the vector equation of a plane.
Solve the system. (1 pt) Solve the system with x(0) = Give your solution in real form. Xi = 1. Describe the trajectory An ellipse with clockwise orientation
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Classify the equilibrium (b) If λί is the eigenvalue with corresponding eigenvector (1,1) and A2 is the eigenvalue with corresponding eigenvector (-1,3), place the three numbers 0, λ, and λ2 in order frorn least to greatest. (c) If ((t), y(t) is the solution satisfying the initial condition (x(0),y(0)- (-2,2). Find i. lim r(t) i. lim rlt) ii. lim y(t) iv. lim y(t) Here is...
1. (20 points total) We will solve the following system of linear equations and express the problem and solution in various forms. 2x1 + 4x2 + x4 – 25 = 1 2.22 - 3.23 – 24 +2.25 = 1. (a) (2 point) How many free parameters are required to describe the solution set? (b) (5 points) Write the problem in the form of an augmented matrix and use Gauss-Jordan elimination to find the reduced echelon form of the matrix. (c)...
3. (16 points) Solve the system of linear congruences using the Chinese Remainder Theorem. 4 (mod 11) a 11 (mod 12) x=0 (mod 13) b. (6 pts) Find the inverses n (mod 11), n21 (mod 12), and nz1 (mod 13). Using these ingredients find the common solution a (mod N) to the system. c. (4 pts) 4. (8 points) What is 1!+ 23+50! congruent to modulo 14?
| (1 pt) Solve the system: 4℃ - 5y = a -3 + 4 = 6 ㅋㅋ