UTMA Linear Systems and Matrices 3

Question 1

What does it mean for a matrix to be singular?

Accepted Answer

Its determinant is 0

Answer

A singular matrix has determinant = 0 and therefore has no inverse.

Question 2

Which of the following represents a linear equation?

Accepted Answer

y = 2x + 5

Answer

y = 2x + 5 has degree 1 in x, making it linear.

Question 3

What is the solution to the system: 2x + 3y = 7 and 4x + 6y = 14?

Accepted Answer

Infinitely many solutions

Answer

The second equation is exactly twice the first, so they are the same line — infinitely many solutions.

Question 4

What is the rank of a 3×3 identity matrix?

Accepted Answer

3

Answer

The 3×3 identity matrix has 3 linearly independent rows, so its rank is 3.

Question 5

Solve: x + 2y + z = 6, x − y + z = 3, 2x + y + 2z = 10. What is the value of y?

Accepted Answer

1

Answer

Subtracting equation 2 from equation 1: 3y = 3 → y = 1.

UTMA - University of Toronto Math Assessment Practice Test