Linear Algebra Multiple-Choice Exam

What is the solution to the system: x + y = 6 and x - y = 2?

• (4, 2)

• (3, 3)

• (2, 4)

• (5, 1)

Solve: 2x + 3y = 12 and x - y = 1

• (3, 2)

• (2, 3)

• (1, 4)

• (4, 1)

Solve the system: x + y + z = 6, 2x - y + z = 3, x + 2y - z = 2

• (1, 2, 3)

• (2, 1, 3)

• (1, 1, 4)

• (0, 2, 4)

In the system: x + 2y = 7, 3x - y = 5, what is the value of x?

• 1

• 2

• 3

• 4

Solve using substitution: x = y + 1, 2x + y = 8

• (2, 1)

• (3, 2)

• (5, 4)

• (4, 3)

The reduced row echelon form of [[1, 2 | 5], [2, 4 | 10]] is:

• No solution

• Infinite solutions

• Unique solution

• Cannot be determined

Gauss-Jordan elimination converts a matrix into:

• Diagonal form

• Row echelon form

• Reduced row echelon form

• Identity matrix

Which operation is not allowed in Gauss-Jordan elimination?

• Switching rows

• Multiplying a row by a constant

• Adding a multiple of one row to another

• Dividing one row by another

If the augmented matrix leads to a row like [0 0 | 5], the system is:

• Consistent

• Inconsistent

• Dependent

• Homogeneous

What is the first step in Gauss-Jordan elimination?

• Make all entries 0

• Make leading entry 1

• Subtract rows

• Switch columns