MAT 343 EXAM 3 (REVIEW)

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1. Find the canonical form and the corresponding change of coordinates for the following linear operators.

$$A=\left( \begin{array}{ccccc} -1 & 1 & 1 & 1 & 1 \\ 2 &... ... 0 & 0 & 0 & 0 & 1\\ 1 & 0 & 0 & 0 & 0 & 0 \end{array}\right)$$

$$D=\left( \begin{array}{ccccc} 4 & 2 & 2 & 2 & 2 \\ 4 & 4... ... & 2 & 2 & 4 & 2\\ 2 & 2 & 2 & 2 & 4\\ \end{array} \right)$$

2. Write the general solution for each of the systems having form

$$\dot x = M x,$$

where $M$ takes values from the previous problem: $A,\;\;B,\;\;C,\;\; D.$