Homework Answers
Determine a, b E R so that the system 6x1 + (2a - 3)x2 + 4ax3...
Determine a, b E R so that the system 6x1 + (2a - 3)x2 + 4ax3 + 3x4 = 2 + b 4x1 + (2a – 2)x2 + 2ax3 + 2x4 = 2 4x1 2x2 + (4a + 2)x3 + (2a + 2)x4 = 0 2x1 - x2 + (2a +3)x3 + 2ax4 = –26 – 2 has (i) a unique solution, (ii) infinitely many solutions, (iii) no solution. Justify your answer !
Thank you! Solve using Gauss-Jordan elimination 2x1 + 6x2 - 26x3 = 18 4x1 + 3x2...
Thank you! Solve using Gauss-Jordan elimination 2x1 + 6x2 - 26x3 = 18 4x1 + 3x2 - 16x3 = 0 x1 + x2 - 5x3 = 1 Select the correct choice below and fill in the answer A) The unique solution is x1=_________, x2 = ________, and x3 - _________. B) The system has infinitely many solutions. The solution is x1 = __________, x2 = _____________, and x3 = t. (Many thanks for the help) Sandi
1. (10+10pts.) Consider the homogeneous system x1 + x2 + (3 – 2a)x3 = 0 2x1...
1. (10+10pts.) Consider the homogeneous system x1 + x2 + (3 – 2a)x3 = 0 2x1 + x2 + 7x3 - 24 = 0 -X2 + 2ax3 + 2x4 = 0 x1 + x2 + 4x3 = 0 where a is a real constant. a. Find the value of a for which the dimension of the solution space of the system is 1. b. Find a basis of the solution space of the system for the value of a found...
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx...
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 72 = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 4. Solve the following system of linear equations using Gauss-Jordan elimination: x1 + x2 - 2.13 + 24 +3.25 = 1 2.x1 - x2 +...
Determine the values of a for which the following system of linear equations has no solutions,...
Determine the values of a for which the following
system of linear equations has no solutions, a unique solution, or
infinitely many solutions. You can select 'always', 'never', 'a =
', or 'a ≠', then specify a value or comma-separated list of
values.
x1+ax2−x3
=
2
−x1+4x2−2x3
=
−5
−2x1+3x2+x3
=
−4
No Solutions:
Unique Solution:
Infinitely Many Solutions:
Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or inf...
Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. ax1−5x2+5x3 = 10 −3x1+4x2−x3 = −9 x1+2x2+7x3 = −6 when does it have.... No Solutions: Many Solutions:
The matrix given is in reduced echelon form 1 0 0 0 1 0-5 0 0...
The matrix given is in reduced echelon form 1 0 0 0 1 0-5 0 0 1 7 C 0 0 0 0 6. Write the system of equations represented by the matrix. (Use x as your variable and label each x with its corresponding column. Enter x_1 for x1, x_2 for x2, x_3 for x3, and x_4 for x4.) = 0 row 1 = 0 row 2 row 3 row 4 0 there is no solution, enter NO SOLUTION.)...
Use the Gaussian elimination method to solve each of the following systems of linear equations. In...
Use the Gaussian elimination method to solve each of the following systems of linear equations. In each case, indicate whether the system is consistent or inconsistent. Give the complete solution set, and if the solution set is infinite, specify three particular solutions. 1-5x1 – 2x2 + 2x3 = 14 *(a) 3x1 + x2 – x3 = -8 2x1 + 2x2 – x3 = -3 3x1 – 3x2 – 2x3 = (b) -6x1 + 4x2 + 3x3 = -38 1-2x1 +...
The augmented matrix is given for a system of equations. If the system is consistent, find...
The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution. [1 2 -3 51 701 4.5 0000] A) x1 = 15+ 11x3 x2 = -5- 4x3 x3 is free C) x1 = 5 - 2x2 + 3x3 x2 = -5- 4x3 X3 is free B) x1 = 5 - 2x2 + 3x3 x2 is free x3 is free D) x1 = 15+ 11x3 x2...
I need the solution of this question asap 3, Cov(X1, X2) = 2, Cov(X2, X3) =...
I need the solution of this question asap
3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, 5. Let Var(x1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Y1, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fyy, y,(91, y2). iii) Suppose Y3 =...
Determine a, b E R so that the system 6x1 + (2a - 3)x2 + 4ax3 + 3x4 = 2 + b 4x1 + (2a – 2)x2 + 2ax3 + 2x4 = 2 4x1 2x2 + (4a + 2)x3 + (2a + 2)x4 = 0 2x1 - x2 + (2a +3)x3 + 2ax4 = –26 – 2 has (i) a unique solution, (ii) infinitely many solutions, (iii) no solution. Justify your answer !
1. (10+10pts.) Consider the homogeneous system x1 + x2 + (3 – 2a)x3 = 0 2x1 + x2 + 7x3 - 24 = 0 -X2 + 2ax3 + 2x4 = 0 x1 + x2 + 4x3 = 0 where a is a real constant. a. Find the value of a for which the dimension of the solution space of the system is 1. b. Find a basis of the solution space of the system for the value of a found...
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 72 = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 4. Solve the following system of linear equations using Gauss-Jordan elimination: x1 + x2 - 2.13 + 24 +3.25 = 1 2.x1 - x2 +...
Determine the values of a for which the following
system of linear equations has no solutions, a unique solution, or
infinitely many solutions. You can select 'always', 'never', 'a =
', or 'a ≠', then specify a value or comma-separated list of
values.
x1+ax2−x3
=
2
−x1+4x2−2x3
=
−5
−2x1+3x2+x3
=
−4
No Solutions:
Unique Solution:
Infinitely Many Solutions:
The matrix given is in reduced echelon form 1 0 0 0 1 0-5 0 0 1 7 C 0 0 0 0 6. Write the system of equations represented by the matrix. (Use x as your variable and label each x with its corresponding column. Enter x_1 for x1, x_2 for x2, x_3 for x3, and x_4 for x4.) = 0 row 1 = 0 row 2 row 3 row 4 0 there is no solution, enter NO SOLUTION.)...
Use the Gaussian elimination method to solve each of the following systems of linear equations. In each case, indicate whether the system is consistent or inconsistent. Give the complete solution set, and if the solution set is infinite, specify three particular solutions. 1-5x1 – 2x2 + 2x3 = 14 *(a) 3x1 + x2 – x3 = -8 2x1 + 2x2 – x3 = -3 3x1 – 3x2 – 2x3 = (b) -6x1 + 4x2 + 3x3 = -38 1-2x1 +...
The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution. [1 2 -3 51 701 4.5 0000] A) x1 = 15+ 11x3 x2 = -5- 4x3 x3 is free C) x1 = 5 - 2x2 + 3x3 x2 = -5- 4x3 X3 is free B) x1 = 5 - 2x2 + 3x3 x2 is free x3 is free D) x1 = 15+ 11x3 x2...
I need the solution of this question asap
3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, 5. Let Var(x1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Y1, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fyy, y,(91, y2). iii) Suppose Y3 =...
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