MATH 2150SEF Linear Algebra
Assignment 1- Autumn 2025
Question 1: A city planner needs to connect two new buildings to the same electrical grid. On a map laid out with a coordinate grid (where each unit is 1 kilometre), the Transformer Station is located at point T(4, 3). The First Building (B) is located at coordinates (1, 7). How long will the direct underground power cable from the Transformer Station to Building B need to be?
Round your final answer to the nearest hundredth of a kilometre. (10 marks)
Question 2: Your phone's battery percentage is recorded at two times:
(1) at 1:00 PM, the battery is at 80% and
(2) at 3:00 PM, the battery is at 40%. Assume the battery drains at a constant rate.
(a) Find the equation that shows battery percentage B after t hours from noon. (4 marks)
(b) What will the battery percentage be at 5:00 PM? (3 marks)
(c) At what time will the battery reach 0%? (3 marks)
Question 3:
A drone flies in two separate movements recorded as vectors: First it moves to meters then to meters.
(a) Draw both vectors on a coordinate plane (starting from origin) (4 marks)
(b) Calculate the length of each displacement. (3 marks)
(c) If the drone made these two movements one after another, what is its final position vector? (3 marks)
Question 4: A boat tries to go directly across a river. The boat's engine produces velocity: km/h (straight east). The river current has velocity: km/h.
(a) Find the boat's resultant velocity relative to the riverbank: (4 marks)
(b) If the boat wants to cancel the current's effect to go straight east, what should be its velocity relative to water: vc (3 marks)
(c) Draw , and on a coordinate plane. (3 marks)
Question 5: A box is pulled along the floor by a force newtons. The box moves through a displacement meters.
(a) Find the dot product (4 marks)
(b) Interpret what this value represents physically (3 marks)
(c) Find the angle between the force and displacement vectors (3 marks)
Question 6: A drone flies in a straight path in 3D space. Its position at any time t is given by Find the points where the drone's flight path intersects:
(a) The ground (XY-plane) - where z=0 (4 marks)
(b)The vertical east wall (YZ-plane) - where x=0 (3 marks)
(c) The vertical north wall (XZ-plane) - where y=0 (3 marks)
Question 7:
(a) Compute det(A) and
(5 marks)
(b) Compute the determinant of matrix
(5 marks)
Question 8: Using the Gauss-Jordan elimination method find the inverse of the matrix:
(10 marks)
Question 9: Solve the following system using row elimination method and find the type of solution: (10 marks)
Question 10: Find the rank of the matrix: (10 marks)