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Q2) Consider the homogeneous system of equations: 3x- 6y + z + 3w 0 a) Find...
Is it possible that all solutions of a homogeneous system of twelve linear equations in fifteen...
Is it possible that all solutions of a homogeneous system of twelve linear equations in fifteen variables are multiples of one fixed nonzero solution? Discuss. Consider the system as Ax = 0, where A is a 12 x 15 matrix. Choose the correct answer below. O A. No. Since A has 12 pivot positions, rank A = 12. By the Rank Theorem, dim Nul A = 12-rank A = 0. Since Nul A = 0, it is impossible to find...
Ax=O Unique solution (trivial solution x-0) No free variables Infinitely many (nontrivial) solutions Some free variable...
Ax=O Unique solution (trivial solution x-0) No free variables Infinitely many (nontrivial) solutions Some free variables Every column of A is pivot column | (=> rank(A) = # of columns of A Some columns of A are not pivot columns rank(A)< #of columns of A You can use the above figure to answer the following questions are about homogeneous systems Ax-0. Answer TRUE or FALSE. If the answer is FALSE, choose FALSE with the appropriate counterexample, i.e example that shows...
Find the complete solution of the system of equations below and write the solutions in the...
Find the complete solution of the system of equations below and write the solutions in the form of x = x + xn, where x, is the particular solution and xn is a solution to the homogeneous system. x – y – 2z + 3w = 4 3x + 2y – z + 2w = 5. -y – 7z + 9w = -2
Consider the following non-homogeneous system of differential equations. a. Write the system in matrix form. b....
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
We were unable to transcribe this imageWe were unable to transcribe this image
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
Consider the system of equations shown below. 3w - 2x + 16y - 22 = -8...
Consider the system of equations shown below. 3w - 2x + 16y - 22 = -8 -w + 5x - 14y + 18251 3w - x + 14y + 22 = 1 (a) Determine whether the nonhomogeneous system Axb is consistent O consistent Inconsistent (b) If the system is consistent, then write the solution in the form x = x + xh where x is a particular solution of Ax=b and is a solution of AX -0. (Ift x =...
Consider the system of equations shown below. 3w - 2x + 16y - 27 = -9...
Consider the system of equations shown below. 3w - 2x + 16y - 27 = -9 -W + 5x - 14y + 18z = 93 3w - x + 14y + 2z = 1 (a) Determine whether the nonhomogeneous system Ax=b is consistent. O consistent Inconsistent (b) If the system is consistent, then write the solution in the form X Xp + Xn, where X, is a particular solution of Ax = b and X, is a solution of AX...
Given the system of equations: +y+z= -6 y - 3x = 8 2x + y +...
Given the system of equations: +y+z= -6 y - 3x = 8 2x + y + 5z = – 19 (a) Determine the type of system: O dependent inconsistent (b) If your answer is dependent, find the complete solution. Write x, y, and z as functions of t, where z = t. If your answer is inconsistent, write DNE in the box for all three variables. 2= y = 2 =
Consider the system of equations shown below. x - 4y + 5z = 8 -7x +...
Consider the system of equations shown below. x - 4y + 5z = 8 -7x + 14y + 4z = -28 3x - 6y + z = 12 If the system is consistent, then write the solution in the form x = xp + xh, where xp is a particular solution of Ax = b and xh is a solution of Ax = 0. (If the system is inconsistent, enter INCONSISTENT in both matrices.) X = [ ] + t...
Q4-Given the following system of equations x-y-z = 6 3x – 3y - 3z = 18...
Q4-Given the following system of equations x-y-z = 6 3x – 3y - 3z = 18 6x – 6y - 6z = 108 How many solution you have in this system? Explain?
Is it possible that all solutions of a homogeneous system of twelve linear equations in fifteen variables are multiples of one fixed nonzero solution? Discuss. Consider the system as Ax = 0, where A is a 12 x 15 matrix. Choose the correct answer below. O A. No. Since A has 12 pivot positions, rank A = 12. By the Rank Theorem, dim Nul A = 12-rank A = 0. Since Nul A = 0, it is impossible to find...
Ax=O Unique solution (trivial solution x-0) No free variables Infinitely many (nontrivial) solutions Some free variables Every column of A is pivot column | (=> rank(A) = # of columns of A Some columns of A are not pivot columns rank(A)< #of columns of A You can use the above figure to answer the following questions are about homogeneous systems Ax-0. Answer TRUE or FALSE. If the answer is FALSE, choose FALSE with the appropriate counterexample, i.e example that shows...
Find the complete solution of the system of equations below and write the solutions in the form of x = x + xn, where x, is the particular solution and xn is a solution to the homogeneous system. x – y – 2z + 3w = 4 3x + 2y – z + 2w = 5. -y – 7z + 9w = -2
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
We were unable to transcribe this imageWe were unable to transcribe this image
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
Consider the system of equations shown below. 3w - 2x + 16y - 22 = -8 -w + 5x - 14y + 18251 3w - x + 14y + 22 = 1 (a) Determine whether the nonhomogeneous system Axb is consistent O consistent Inconsistent (b) If the system is consistent, then write the solution in the form x = x + xh where x is a particular solution of Ax=b and is a solution of AX -0. (Ift x =...
Consider the system of equations shown below. 3w - 2x + 16y - 27 = -9 -W + 5x - 14y + 18z = 93 3w - x + 14y + 2z = 1 (a) Determine whether the nonhomogeneous system Ax=b is consistent. O consistent Inconsistent (b) If the system is consistent, then write the solution in the form X Xp + Xn, where X, is a particular solution of Ax = b and X, is a solution of AX...
Given the system of equations: +y+z= -6 y - 3x = 8 2x + y + 5z = – 19 (a) Determine the type of system: O dependent inconsistent (b) If your answer is dependent, find the complete solution. Write x, y, and z as functions of t, where z = t. If your answer is inconsistent, write DNE in the box for all three variables. 2= y = 2 =
Q4-Given the following system of equations x-y-z = 6 3x – 3y - 3z = 18 6x – 6y - 6z = 108 How many solution you have in this system? Explain?
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