Use projection matrices to find the matrix exponential and particular solution of the given linear system x' = Ax + f(t), x(a) = x3. 7 X(0) = 3 - 1 3 x' = x, f(t) = - 3 - 2 ..... Find the projection matrix(matrices) for A. 1 0 The projection matrix(matrices) is/are 0 1 (Type exact answers, using radicals and i as needed. Use a comma to separate matrices as needed.) Find the matrix exponential. 1+ 3t - t e At - 9t 1-3t Find the particular solution to the initial value problem. X(t) =

College Algebra (MindTap Course List)
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ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
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Use projection matrices to find the matrix exponential and particular solution of the given linear system x' = Ax + f(t), x(a) = x3.
7
X(0) =
3
- 1
3
x' =
x, f(t) =
- 3
- 2
.....
Find the projection matrix(matrices) for A.
1 0
The projection matrix(matrices) is/are
0 1
(Type exact answers, using radicals and i as needed. Use a comma to separate matrices as needed.)
Find the matrix exponential.
1+ 3t
- t
e At -
9t 1-3t
Find the particular solution to the initial value problem.
X(t) =
Transcribed Image Text:Use projection matrices to find the matrix exponential and particular solution of the given linear system x' = Ax + f(t), x(a) = x3. 7 X(0) = 3 - 1 3 x' = x, f(t) = - 3 - 2 ..... Find the projection matrix(matrices) for A. 1 0 The projection matrix(matrices) is/are 0 1 (Type exact answers, using radicals and i as needed. Use a comma to separate matrices as needed.) Find the matrix exponential. 1+ 3t - t e At - 9t 1-3t Find the particular solution to the initial value problem. X(t) =
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