UTMA Linear Systems and Matrices

Question 1

What is the solution to the system: x + y = 5 and x − y = 1?

Accepted Answer

x=3, y=2

Answer

Adding the equations: 2x = 6 → x = 3; substituting: y = 5 − 3 = 2.

Question 2

What is the determinant of the matrix [[2, 3],[1, 4]]?

Accepted Answer

5

Answer

det = 2×4 − 3×1 = 8 − 3 = 5.

Question 3

Which method eliminates a variable by multiplying equations?

Accepted Answer

Elimination

Answer

The elimination method multiplies equations by constants to cancel a variable when added.

Question 4

How many solutions does the system y = 2x + 1 and y = 2x − 3 have?

Accepted Answer

None

Answer

Both lines have slope 2 but different y-intercepts, so they are parallel and never intersect.

Question 5

What is the product of matrices A = [[1,0],[0,1]] and B = [[3,4],[5,6]]?

Accepted Answer

[[3,4],[5,6]]

Answer

The identity matrix I times any matrix B equals B.

UTMA - University of Toronto Math Assessment Practice Test