Question

1. For the matrix $A = \begin{pmatrix} -1 & 10 \\ 0 & 3 \end{pmatrix}$, find $e^{At}$ using modal decomposition.

          1. For the matrix $A = \begin{pmatrix} -1 & 10 \\ 0 & 3 \end{pmatrix}$, find $e^{At}$ using modal decomposition.
        
1. For the matrix A = 
    < p m a t r i x >, find e^At using modal decomposition.

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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1.For the matrix A= 10 0 3 find eAt using modal decomposition
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Transcript

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00:01 In this question, we are asked to find the matrix a so that a times 2, 3, 1, 2, 2 ,000, equals to the identity matrix.
00:10 In other words, we are asked to find the inverse of the matrix 2, 3, 1 2.
00:17 Now, to find the inverse, let's call this matrix b.
00:21 And basically, we are asked to find b inverse here.
00:25 And to find b inverse, we need to calculate 1 over the determinant of b.
00:34 And then we need to switch the entries on the main diagonal, and in our case they are same, so it's not going to make any difference, and multiply the entries on the other diagonal by negative 1...
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