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9:46 < Evaluation3 - MTH1... Evaluation 3 - MTH1106 23-4 Thursday, 23 November 2023 7:39 am Question 1 A car leaves Georgetown and travels for a number of miles to a point A and then travels for a further number of miles to a point B. (a) Represent the car's change in location with two vectors-vectors a and b. (b) Write the two vectors above in component form. (c) Determine the resultant vector in component form. (d) Hence, determine the length of this resultant vector. (e) Are vectors a and b perpendicular? Prove algebraically. (f) If the car then retraces its path from point B to point A, represent this position change with vector c. State vector c. Question 2 Identify and state a problem that requires a linear system of two equations for its solution. (a) State the linear system. (b) Write the linear system in matrix form. (c) Hence, solve this matrix equation by first determining and applying the inverse of the coefficient matrix. (d) What is the determinant of the coefficient matrix? (e) is the coefficient matrix a singular matrix? Why or why not? If it is or was, how would this affect the solution of the linear system? (f) If a system of three linear equations was involved, would the computation of the determinant be different? Explain. Deliverables You are to upload a word processing document (not PDF) to Moodle. This evaluation is to be completed in groups of three(3). The submission date is Wednesday November 29 at noon. There will be an Oral Defence of concepts applied in the Evaluation. A schedule for Oral defence of the Evaluation will be discussed. = III New Section 1 Page 1 1/1 0 9:46 < Evaluation3 - MTH1... Evaluation 3 - MTH1106 23-4 Thursday, 23 November 2023 7:39 am Question 1 A car leaves Georgetown and travels for a number of miles to a point A and then travels for a further number of miles to a point B. (a) Represent the car's change in location with two vectors-vectors a and b. (b) Write the two vectors above in component form. (c) Determine the resultant vector in component form. (d) Hence, determine the length of this resultant vector. (e) Are vectors a and b perpendicular? Prove algebraically. (f) If the car then retraces its path from point B to point A, represent this position change with vector c. State vector c. Question 2 Identify and state a problem that requires a linear system of two equations for its solution. (a) State the linear system. (b) Write the linear system in matrix form. (c) Hence, solve this matrix equation by first determining and applying the inverse of the coefficient matrix. (d) What is the determinant of the coefficient matrix? (e) is the coefficient matrix a singular matrix? Why or why not? If it is or was, how would this affect the solution of the linear system? (f) If a system of three linear equations was involved, would the computation of the determinant be different? Explain. Deliverables You are to upload a word processing document (not PDF) to Moodle. This evaluation is to be completed in groups of three(3). The submission date is Wednesday November 29 at noon. There will be an Oral Defence of concepts applied in the Evaluation. A schedule for Oral defence of the Evaluation will be discussed. = III New Section 1 Page 1 1/1 0