First calculate the operational determinant of the given system in order to determine how many arbitrary constants should appear in a general solution. Then attempt to solve the system explicitly. (D²+1)x-2D2y=2e (D²-1)x+2D2y=0

Explain why we can always evaluate the determinant of a square matrix.

The determinant of 22 matrix A is 3. If you switch the rows and multiply the first row by 6 and the second row by 2, explain how to find the determinant and provide the answer.

Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?

Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.

Explain how to decide which row or column you will use to expand a 33 determinant.

Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.

Explain the difference between a square matrix and its determinant. Give an example of each.

What operations can be performed on a linear system to arrive at an equivalent system?

Use Cramers Rule to solve the system of linear equations for x and y. kx+(1k)y=1(1k)x+ky=3 For what values of k will the system be inconsistent?