Kramer's Rule and Determinants

This video tutorial explains how to use Kramer's Rule to solve a system of linear equations with two variables. It covers the calculation of the determinant D, and the matrices Dx and Dy, followed by solving for the variables X and Y. The tutorial includes a detailed example to reinforce the learning process.

What is the primary purpose of using Kramer's Rule?

• To calculate the area of a triangle

• To solve a system of linear equations

• To find the roots of a polynomial

• To solve quadratic equations

In the first example, what is the value of the determinant D?

• 99

• -99

• 33

• -33

What is the formula for calculating Dx in Kramer's Rule?

• Replace coefficients of y with constants

• Replace coefficients of x with constants

• Use the original coefficients of x and y

• Replace all coefficients with zero

What is the value of x in the first example after applying Kramer's Rule?

• 1

• 2

• 3

• 4

What is the solution for the system of equations in the first example?

• (3, 4)

• (5, 2)

• (4, 3)

• (2, 5)

In the second example, what are the coefficients of x in the equations?

• 4 and 5

• 2 and 5

• 3 and 4

• 1 and 6

What is the determinant D for the second example?

• 5

• 10

• -10

• -5

How do you calculate Dy in Kramer's Rule?

• Replace coefficients of x with constants

• Replace coefficients of y with constants

• Use the original coefficients of x and y

• Replace all coefficients with zero

What is the value of y in the second example after applying Kramer's Rule?

• 6

• 5

• 4

• 3

What is the solution for the system of equations in the second example?

• (5, 2)

• (4, 3)

• (3, 4)

• (2, 5)