(a) when the system (4) above is put into the form v′ = av, what is the matrix a? (b) enter the matrix a into matlab, and record the input and output for this in your word document. use matlab to find the characteristic roots (eigenvalues) and characteristic vectors (eigenvectors) of your matrix a. copy and paste all input and output from your command into your word document. (c) use the formula (2) above and the results from part (b) to write the general solution of our system (4). write this solution in your document. what happens to the system as t gets large? (d) use pplane to create a plot of the solutions. as in the example, choose options -> solution direction -> forward and click on the plot several times. include this plot in your writeup. does this match your answer to (c)?

1jessica's home town is a mid-sized city experiencing a decline in population. the following graph models the estimated population if the decline continues at the same rate. select the most appropriate unit for the measure of time that the graph represents. a. years b. hours c. days d. weeks

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24

What is the area of the original rectangle? 8 cm² 20 cm² 25 cm² 40 cm²