Determinants and Kramer's Rule

This video tutorial explains Kramer's Rule, a method for solving systems of linear equations. It covers both two-variable and three-variable systems, detailing how to calculate determinants and apply them to find solutions. The video includes step-by-step examples and encourages viewers to practice the method for mastery.

What is the determinant of a 2x2 matrix with elements a1, a2, b1, and b2?

• a2*b2 - a1*b1

• a2*b1 - a1*b2

• a1*b2 - a2*b1

• a1*b1 - a2*b2

In Kramer's Rule, how do you calculate dx for a two-variable system?

• Replace coefficients of y with constants

• Replace coefficients of x with constants

• Replace both coefficients with constants

• Use the original coefficients

What is the value of x in the system: 2x + 3y = 13 and 3x - 5y = -9?

• 1

• 2

• 3

• 4

What is the determinant of the matrix for the system: 2x - 7y = 1 and 3x + y = 13?

• 27

• 21

• 23

• 25

How do you set up the matrix for dx in a three-variable system?

• Use the original coefficients

• Replace coefficients of x with constants

• Replace coefficients of z with constants

• Replace coefficients of y with constants

What is the determinant of a 3x3 matrix with elements a1, a2, a3, b1, b2, b3, c1, c2, c3?

• a1(b2c3 - b3c2) - b1(a2c3 - a3c2) + c1(a2b3 - b2a3)

• a1(b3c2 - b2c3) - b1(a3c2 - a2c3) + c1(a3b2 - b3a2)

• a1(b3c2 - b2c3) + b1(a3c2 - a2c3) - c1(a3b2 - b3a2)

• a1(b2c3 - b3c2) + b1(a2c3 - a3c2) - c1(a2b3 - b2a3)

What is the value of z in the system: 3x - 2y + z = 2, 4x + 3y - 2z = 4, 5x - y + 3z = 8?

• 3

• 4

• 2

• 1

In Kramer's Rule, what is the formula for calculating y in a three-variable system?

• dy/d

• dx/d

• dz/d

• d/dy

What is the value of y in the system: 3x - 2y + z = 2, 4x + 3y - 2z = 4, 5x - y + 3z = 8?

• 3

• 2

• 4

• 1

What is the final step in verifying the solution of a system using Kramer's Rule?

• Substitute the values back into the original equations

• Use another method to solve the system

• Check if the determinant is zero

• Recalculate the determinants