Verify that V = x14+ 2x22+2x1x2 + x12 is a Lyapunov function for the system described by the following state  equations dx1/dt = x2 dx2/dt= -x2 - x13. Then, check the stability of the system.

Show that the linear system has at least one solution for any values b1, b2, b3. -4y1 Y2 буз + 7у4 b₁ -8y₁ + 6y2 Y3 +9y4 b₂ 6y1 11y2 3y3 + 2y4 =b3 = =

Let x1 and x2 be two different solutions of the following linear equation system. Here, if x1 = (1,1,-3,1), x2 = x1 + xd, find all xd where C^Tx2 - C^Tx1 = 1 However, c^T = [1 1 2 1].

The table below shows the projected values (in millions of dollars) of hardback college textbooks sold in the United States for the years 2007 to 2009. Year Value 2007 4412 C = 2008 4471 2009 4556 (a) Create a system of linear equations for the data to fit the curve y = at² + bt + c, where t is the year and t = 7 corresponds to 2007, and y is the value of the textbooks. = 4412 = 4471 = 4556 (b) Use Cramer's Rule to solve your system. a = b =