Solve the following matrix differential equation:
= Ax
where A= [ 5 1 ; -2 -2]
and x0 =[-3; 8]
Solve the following matrix differential equation: = Ax where A= [ 5 1 ; -2 -2]...
Let Ax=b be a matrix equation where A is given by 11 -2 3 2 1 and b by 3 1 2 1) Show that the equation is inconsistent. (15 points) 2) Find the least squares solution x"hat" of the equation and compute the error. (15 points)
b) i. Form partial differential equation from z = ax - 4y+b [4 marks] a +1 ii. Solve the partial differential equation 18xy2 + sin(2x - y) = 0 дх2ду c) i. Solve the Lagrange equation [4 Marks] az -zp + xzq = y2 where p az and q = ду [5 Marks] x ax ii. A special form of the second order partial differential equation of the function u of the two independent variables x and t is given...
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6 when 0 (1 point) The differential equation can be written in differential form: M(x, y) dz +N(z, ) dy-0 where ,and N(x, y)--y5-3x The term M(, y) dz + N(x, y) dy becomes an exact differential if the left hand side above is divided by y4. Integrating that new equation, the solution of the differential equation is E C
a) Write the augmented matrix for the linear system that corresponds to the matrix equation AX = b b) solve the above system c) write the solution as a vector A= 0 4 5 -1 3 2 and b= 1 24 5 4 2
1. Solve the following Differential Equations. 2. Use the variation of parameters method to find the general solution to the given differential equation. 3. a) y" - y’ – 2y = 5e2x b) y" +16 y = 4 cos x c) y" – 4y'+3y=9x² +4, y(0) =6, y'(0)=8 y" + y = tan?(x) Determine the general solution to the system x' = Ax for the given matrix A. -1 2 А 2 2
a=1 b=3 7. Solve the differential equation: x x + (ax – 7)y = bx? (Note: Where a and b are any two numbers of your MEC ID No. and a, b>0) (9 marks)
we assume that X solves the differential equation X'=AX. In this problem, we will investigate the strategy to deal with repeated eigenvalues. Conside:r A=17-2-6 1. This matrix has only one eigenvalue Ao of multiplicity 3. Find the characteristic equation, the eigenvalue λ0 and an eigenvector P for λ0 2. Find vectors K. L such that (A-X0IK-P and (A-X01)L-K. Compute the matrix M-1AM where M-(PIKL) 3. Let Y -M'X. Solve the equation for Y in the following manner : first, solve...
Use the definition of Ax to write the vector equation as a matrix equation. 7 -5 -9 3 5 7 1 X1 + X2 +X3 -4 -4 - 7 7 -9 8 -3 4 X1 3 1 X2 7 X₂ (Type an integer or simplified fraction for each matrix element.)
b, where b 8. For each matrix A in Exercise 7, solve AX [10, 10, 10). Use elimination by pivoting to find the inverse of the following matri- ces. 2 -3 2. - - 1 (a) 1 1 (b) 2 2 - 4 - 1 5 4 -2 3 ذرا 2 2 4 -2] - 4 (c) 2 1 w (d) 1 - 2 5 4. 6 2 -1 -3 4 2 2 1 3 3 -3 -5 6 -2...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...