Homework Answers
Let A = ( a1 0 ... 0 0 a2 ... 0 ... ... ... 0...
Let
A = ( a1 0 ... 0
0 a2 ... 0
... ... ...
0 0 an)
be an n * n matrix, where a1, a2, . . . , an are
nonzero real numbers.
(a) Find the general solution to the system of equations ->
->
x' = A * x
(b) Solve the initial value problem x1(0) =
x2(0) = · · · = xn(0) = k, for some constant
k.
(c) Solve the initial value problem
(x1(0) x2(0)...
Question 2 Find the general solution to 21 2 -2 X1 X2 1 4 32 Enter...
Question 2 Find the general solution to 21 2 -2 X1 X2 1 4 32 Enter Answer D Question 3 Find the solution to the initial value problem X1 1 -2 21 2] [3 (2:0) = [] X1(0) 22(0) X2 3 6 X2 Enter Answer Question 2 Find the general solution to 21 2 -2 X1 X2 1 4 32 Enter Answer D Question 3 Find the solution to the initial value problem X1 1 -2 21 2] [3 (2:0)...
1 1 1 0 -5 0 -77 0 2. 0 2 2. Let A be a...
1 1 1 0 -5 0 -77 0 2. 0 2 2. Let A be a 4 x 5 matrix whose reduced row echelon form is R 0 0 0 3 LO 0 0 0 0 For parts (b) and (c), write the solution in parametric vector form. (a) (2 points) Is the equation Ax b consistent for all b in R4? Why or why not? (b) (4 points) Solve the equation Ax = 0. 4 -3 -3 (c) (3...
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...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i + 2, for i = 0, . . . , 3. Given the divided difference...
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i
+ 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1,
f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the
data point (0, 3), find a Newton form for the Lagrange polynomial
interpolating all 5 data points.
3. (25 pts) Let (r,, f()), 0,3, be data...
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a gen...
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)-
(1 point) Consider the initial value problem -51เซี. -4 มี(0)...
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.)...
Find the solution to the initial value problem X1 1 -2 [] X1 (0) X2(0) X2...
Find the solution to the initial value problem X1 1 -2 [] X1 (0) X2(0) X2 6
5 X1 X2 0 0 1. 51 2.5 2 1 I 3 T 2 I 27...
5 X1 X2 0 0 1. 51 2.5 2 1 I 3 T 2 I 27 Suggested model to correlate the data has the following form: y= 0o+ a1x1 + a2 X2 It is desired to find the three coefficients do, a1 and a2 (a) What are the three equations required to find do, a1 and a2. Put them in matrix form DONT SOLVE
Let
A = ( a1 0 ... 0
0 a2 ... 0
... ... ...
0 0 an)
be an n * n matrix, where a1, a2, . . . , an are
nonzero real numbers.
(a) Find the general solution to the system of equations ->
->
x' = A * x
(b) Solve the initial value problem x1(0) =
x2(0) = · · · = xn(0) = k, for some constant
k.
(c) Solve the initial value problem
(x1(0) x2(0)...
Question 2 Find the general solution to 21 2 -2 X1 X2 1 4 32 Enter Answer D Question 3 Find the solution to the initial value problem X1 1 -2 21 2] [3 (2:0) = [] X1(0) 22(0) X2 3 6 X2 Enter Answer Question 2 Find the general solution to 21 2 -2 X1 X2 1 4 32 Enter Answer D Question 3 Find the solution to the initial value problem X1 1 -2 21 2] [3 (2:0)...
1 1 1 0 -5 0 -77 0 2. 0 2 2. Let A be a 4 x 5 matrix whose reduced row echelon form is R 0 0 0 3 LO 0 0 0 0 For parts (b) and (c), write the solution in parametric vector form. (a) (2 points) Is the equation Ax b consistent for all b in R4? Why or why not? (b) (4 points) Solve the equation Ax = 0. 4 -3 -3 (c) (3...
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...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i
+ 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1,
f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the
data point (0, 3), find a Newton form for the Lagrange polynomial
interpolating all 5 data points.
3. (25 pts) Let (r,, f()), 0,3, be data...
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)-
(1 point) Consider the initial value problem -51เซี. -4 มี(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.)...
Find the solution to the initial value problem X1 1 -2 [] X1 (0) X2(0) X2 6
5 X1 X2 0 0 1. 51 2.5 2 1 I 3 T 2 I 27 Suggested model to correlate the data has the following form: y= 0o+ a1x1 + a2 X2 It is desired to find the three coefficients do, a1 and a2 (a) What are the three equations required to find do, a1 and a2. Put them in matrix form DONT SOLVE
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