Solved: In 1 and 2 fill in the blanks.

Chapter , Problem 2RP

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In Problems 1 and 2 fill in the blanks

The vector \(\mathbf{X}=c_{1}\left(\begin{array}{r} -1 \\ 1 \end{array}\right) e^{-9 t}+c_{2}\left(\begin{array}{l} 5 \\ 3 \end{array}\right) e^{7}\) is solution of the initial-value problem \(\mathbf{X}^{\prime}=\left(\begin{array}{rr} 1 & 10 \\ 6 & -3 \end{array}\right) \mathbf{X}, \mathbf{X}(0)=\left(\begin{array}{l} 2 \\ 0 \end{array}\right)\) for \(c_{1}\) = __________ and \(c_{2}\) = __________.

Text Transcription:

mathbf X = c_1 ({array} r -1 1 {array}) e^-9 t+c_2 ({array} l 5 3 {array}) e^7

mathbf X^prime = ({array} rr 1 & 10 6 & -3 {array}) mathbf X, mathbf X 0 = ({array} l 2 0 {array})

c_1

c_2

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