Recurrence Relations and Solutions

The video tutorial explains how to solve a recurrence relation using the characteristic root technique. It begins by setting up the recurrence relation and transforming it into a characteristic equation. The equation is solved by factorization, yielding two distinct roots. The general solution is derived using these roots, and initial conditions are applied to find specific constants. An augmented matrix method is used to solve the system of equations for these constants. The tutorial concludes by presenting the final closed formula for the recurrence relation.

What is the initial condition for a sub 0 in the given recurrence relation?

• 0

• 2

• 10

• 6

What technique is used to solve the recurrence relation?

• Matrix method

• Characteristic root technique

• Graphical method

• Trial and error

What is the value of alpha in the standard form of the recurrence relation?

• -8

• 8

• 6

• -6

What is the characteristic equation derived from the recurrence relation?

• x^2 - 8x + 6 = 0

• x^2 - 6x + 8 = 0

• x^2 + 6x + 8 = 0

• x^2 + 8x + 6 = 0

What are the roots of the characteristic equation?

• x = -4, x = 2

• x = 4, x = -2

• x = -4, x = -2

• x = 4, x = 2

What is the form of the general solution for the recurrence relation?

• a sub n = a * 4^n + b * 2^n

• a sub n = a * (-4)^n + b * (-2)^n

• a sub n = a * 2^n + b * 4^n

• a sub n = a * (-2)^n + b * (-4)^n

What equation is formed using the initial condition a sub 0 = 2?

• a - b = 10

• a + b = 2

• a - b = 2

• a + b = 10

What is the equation derived from the initial condition a sub 1 = 10?

• 4a + 2b = 10

• 4a - 2b = 10

• -4a - 2b = 10

• -4a + 2b = 10

What is the value of 'a' after solving the system of equations?

• 9

• -7

• 10

• 2

What is the value of 'b' after solving the system of equations?

• 2

• 10

• -7

• 9