Let ? and ? be two parameters. Write the equation system x1 - s = –x3...
Let ? and ? be two parameters. Write the equation system x1 - s = –x3 3x3 + 3x1 = –x2 rx3 + x2 = x1 on the form:b) We look at the equation system above. i) Calculate it (A) and show what value r must have for the equation system to have exactly one solution. ii) Show what values r and s must have for the system of equations to have infinitely many solutions. iii) Show what values r and s must have for the equation system to have no solution. c) Let F, G and H be three n × n matrices. Solve the following equation with respect to X, when it is known that the matrix F - G2 is invertible. F(F + X) = G2(X + H)
b) We look at the equation system above.
i) Calculate it (A) and show what value r must have for the equation system to have
exactly one solution.
ii) Show what values r and s must have for the system of equations to have infinitely many
solutions.
iii) Show what values r and s must have for the equation system to have no solution.
c) Let F, G and H be three n × n matrices. Solve the following equation with respect to X, when it is
known that the matrix F - G2 is invertible.
F(F + X) = G2(X + H)Homework Answers
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Let ? and ? be two parameters.
Write the equation system
x1 - s = –x3...
I will show the whole task here. I need a solution for task C C. let...
I will show the whole task here. I need a solution for
task C
C. let F, G, and H be three n x n matrices. Solve the
following equation with consideration on X, when it is known that
matrix F – G2 is invertible.
F(F+X) = G2(X+H)
5. let t and r be two parameters. a. Write the equationssystem X-S=-X3 3x3 + 3x1 = -X2 rX3 + x2 = X1 On the form: i) A x= ii) 7. x1...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 -...
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0...
Write the system of equations as a matrix equation of the form AX = B. X1...
Write the system of equations as a matrix equation of the form AX = B. X1 - 2x2 + 3x3 = - 4 - 2X1 + 4x2 = 1 X1 + X2 + 3x3 = - 3 X1 X2 = X3 (Type an integer or decimal for each matrix element.)
(1 point) Solve the system x +x2 x2 +x3 X1 +X4 X1 X2 X3 X4 +s
(1 point) Solve the system x +x2 x2 +x3 X1 +X4 X1 X2 X3 X4 +s
Suppose that X1, X2, X3 and X4 are independent Poisson where E[X1] = lab E[X2] =...
Suppose that X1, X2, X3 and X4 are independent Poisson where E[X1] = lab E[X2] = 11 – a)b E[X3] = da(1 – b) E[X2] = X(1 — a)(1 – b) for some a and b between 0 and 1. Let S = X1 + X2+X3+X4, R= X1 + X2 and C = X1 + X3. (a) Find P(R = 10) (b) Find P(X1 = 6 S = 16 and R= 12). (c) Suppose we want to condition on the...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
2. Write the solution of the linear system -X1 – 24 +225 = -2 3x1 +...
2. Write the solution of the linear system -X1 – 24 +225 = -2 3x1 + x2 + 2x3 + 4x4 – 25 = 1 421 – x2 + x3 + 2x5 = 1 in the form x = Ep + Xh where xp is a particular solution and Xh is a solution of the corresponding homogeneous system.
Problem #5 -- Consider the following linear programming problem: Maximize Z = 2x1 + 4x2 +...
Problem #5 -- Consider the following linear programming problem: Maximize Z = 2x1 + 4x2 + 3x3 subject to: X1 + 3x2 + 2x3 S 30 best to X1 + x2 + x3 S 24 3x1 + 5x2 + 3x3 5 60 and X120, X220, X3 2 0. You are given the information that x > 0, X2 = 0, and x3 >O in the optimal solution. Using the given information and the theory of the simplex method, analyze the...
Write the given system of equations as a matrix equation and solve by using inverses. -3x,...
Write the given system of equations as a matrix equation and solve by using inverses. -3x, + X2 = k1 7X, - X2 + Xz = K₂ + z = k3 3x1 a. What are xy, X2, and X3 when ky = - 9, ky = - 4, and kz = 8? = X1 X2 X= b. What are X7, Xy, and Xz when k, = -10, ky = 10, and kz =5? X1 = X2 = Xz = c....
I will show the whole task here. I need a solution for
task C
C. let F, G, and H be three n x n matrices. Solve the
following equation with consideration on X, when it is known that
matrix F – G2 is invertible.
F(F+X) = G2(X+H)
5. let t and r be two parameters. a. Write the equationssystem X-S=-X3 3x3 + 3x1 = -X2 rX3 + x2 = X1 On the form: i) A x= ii) 7. x1...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0...
Write the system of equations as a matrix equation of the form AX = B. X1 - 2x2 + 3x3 = - 4 - 2X1 + 4x2 = 1 X1 + X2 + 3x3 = - 3 X1 X2 = X3 (Type an integer or decimal for each matrix element.)
(1 point) Solve the system x +x2 x2 +x3 X1 +X4 X1 X2 X3 X4 +s
Suppose that X1, X2, X3 and X4 are independent Poisson where E[X1] = lab E[X2] = 11 – a)b E[X3] = da(1 – b) E[X2] = X(1 — a)(1 – b) for some a and b between 0 and 1. Let S = X1 + X2+X3+X4, R= X1 + X2 and C = X1 + X3. (a) Find P(R = 10) (b) Find P(X1 = 6 S = 16 and R= 12). (c) Suppose we want to condition on the...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
2. Write the solution of the linear system -X1 – 24 +225 = -2 3x1 + x2 + 2x3 + 4x4 – 25 = 1 421 – x2 + x3 + 2x5 = 1 in the form x = Ep + Xh where xp is a particular solution and Xh is a solution of the corresponding homogeneous system.
Problem #5 -- Consider the following linear programming problem: Maximize Z = 2x1 + 4x2 + 3x3 subject to: X1 + 3x2 + 2x3 S 30 best to X1 + x2 + x3 S 24 3x1 + 5x2 + 3x3 5 60 and X120, X220, X3 2 0. You are given the information that x > 0, X2 = 0, and x3 >O in the optimal solution. Using the given information and the theory of the simplex method, analyze the...
Write the given system of equations as a matrix equation and solve by using inverses. -3x, + X2 = k1 7X, - X2 + Xz = K₂ + z = k3 3x1 a. What are xy, X2, and X3 when ky = - 9, ky = - 4, and kz = 8? = X1 X2 X= b. What are X7, Xy, and Xz when k, = -10, ky = 10, and kz =5? X1 = X2 = Xz = c....
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