CSU11001 Sample In-Class Test 2024 PDF
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Trinity College Dublin
2024
Trinity College Dublin
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Summary
This is a sample in-class test for CSU11001 at Trinity College Dublin, 2024. It covers linear algebra topics, including parametric equations and Gaussian elimination. The test contains multiple questions with varying marks.
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CSU11001 SAMPLE IN-CLASS TEST 2024 This test is worth 20% of your final grade for this module. All questions carry equal marks. You have 50 minutes to complete this test. Use of a calculator is not permitted. Q1 The parametric equation of a plane is given by...
CSU11001 SAMPLE IN-CLASS TEST 2024 This test is worth 20% of your final grade for this module. All questions carry equal marks. You have 50 minutes to complete this test. Use of a calculator is not permitted. Q1 The parametric equation of a plane is given by x = 3 + 1s + 4t y = 2 + 3s − 2t z = −1 + 2s + 3t Find a vector that is perpendicular to the plane. [4 marks] Q2 Determine whether the line with parametric equations x = 1 + 1t y = 1−t z = 2+t intersects with the plane with equation x + 2y + z − 10 = 0. If it does intersect, find the point of intersection. If it doesn’t intersect, explain why uinsg a full sentence. [4 marks] 1 3 −2 1 0 2 Q3 P = 4 2 1 and Q = −1 2 −1. What is (3P −2Q)T ? 1 0 1 3 −2 1 [4 marks] Q4 Solve the following linear system using Gaussian Elimination: 3x + 2y + z = 13 x +y +z = 3 2x + y + 2z = 4 [4 marks] 1 0 5 Q5 Use Gaussian Elimination to find the inverse of the matrix 2 1 6 3 4 0 [4 marks]
