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Linear Algebra Midterm Exam Outlines

This document outlines the topics covered in the linear algebra midterm exam. It includes multiple-choice questions, true or false statements, computations, mathematics proofs, and algorithm design problems.

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Linear Algebra Midterm Exam Outlines

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  1. Midterm IIOutline Shang-Hua Teng

  2. Problem 1: Multiple Choices12 points • There might be more than one correct answers; • So you should try to mark them all. • 1 question on the four vector spaces defined by a matrix • 1 question on matrix multiplication. • 1 question on orthogonality

  3. Problem 2. True or false and justify16 points • Four questions on • Orthogonal subspaces • Column/row spaces • Orthonormal matrices • Projection matrices

  4. Problem 3. Computations40 points • One question of least-square approximation and/or line fitting • One question of Gram-Schmidt Process and QR decomposition • One question on determinant of matrix and Cramer Rule for solving linear systems

  5. Problem 4: Mathematics10 points • One problem on proving a statement on matrix inverse and matrix transpose

  6. Problem 5: Algorithm Design22 points • One problem related with orthogonal complement of a vector space. Your will be asked to describe your algorithms and analysis the complexity of your algorithms

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