What is the name of the method that uses matrices to solve a system of linear equations?

• Substitution method
• Elimination method
• Matrix method
• Graphing method

True or False: In a 2x2 matrix, there are two rows and two columns.

If the determinant of a 2x2 matrix is zero, can you use the matrix method to solve the equations?

Which step comes first when solving simultaneous equations with matrices?

• Find the inverse of the matrix
• Write the equations in matrix form
• Multiply matrices
• Calculate the determinant

True or False: The inverse of a matrix is used to solve for the variables in simultaneous equations.

What is the formula for the determinant of a 2x2 matrix [[a, b], [c, d]]?

• ad - bc

Which of the following systems can be represented by a 2x2 matrix?

• 3x + 2y + z = 7, x - y + z = 2
• x + y = 5, 2x - y = 3
• x = 4
• x + y + z = 6, x - z = 1

Cramer's Rule can only be used to solve systems of equations where the number of equations equals the number of unknowns.

Which of the following is NOT true about Cramer's Rule?

• It uses determinants to solve equations.
• It can be used for any number of equations and unknowns.
• It gives a unique solution if the determinant is not zero.
• It involves replacing columns of the matrix with constants.

If you use Cramer's Rule to solve for variable x in a 2x2 system, which determinant do you divide by the main determinant?

• Determinant of the y-column replaced
• Determinant of the x-column replaced
• Sum of all determinants
• Determinant of the original matrix

Cramer's Rule can be used even if the determinant of the coefficient matrix is zero.

What is the first step when using the inversion matrix method to solve simultaneous equations?

• Find the inverse of the matrix
• Write the equations in matrix form
• Multiply both sides by the inverse
• Add the equations together

If the determinant of the coefficient matrix is zero, the inversion matrix method can still be used to solve the system.

Which of the following represents the correct formula for solving AX = B using the inversion matrix method?

• X = AB
• X = BA⁻¹
• X = A⁻¹B
• X = B⁻¹A

The inversion matrix method can only be used when the number of equations is equal to the number of unknowns.