1111_08rev - MATH1111/08Fall/Self-assessment 1 MATH1111...

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MATH1111/08Fall/Self-assessment 1 MATH1111 - Revision note The note is to serve as a guideline for your revision. It is by no means complete and certainly does not cover everything taught in the course. Even though no mention here, you may necessarily look up from the textbook or any relevant materials for your understanding. 1. System of linear equation (a) How to Solve? By Gaussian elimination. (See lecture 2) (b) How many types of the solution? How to determine? See lecture 2 2. Matrices (a) What are the arithmetics of matrices? Addition, subtraction, scalar multiplication, matrix multiplication, transpose (See lectures 3 & 4) (b) How to represent a system of linear equations in matrix form? What is meant by the inverse of a matrix? See lecture 5 (c) What operations in matrix do elementary row operations correspond? See lecture 5 & 6 (d) Use elementary row operations to find inverse and conditions for nonsingularity See lecture 7. In addition to the method, you should know why the method works. 3. Determinant (a) What’s the definition? See lecture 8 (b) What properties of determinant do you know? What s the relation between the nonsingu- larity and determinant? And why? See lecture 9 (c) What is the adjoint of a matrix? What do you know about it? See lecture 9. Note that the relation A (adj A ) = (det A ) I provides an alternative method to find inverses.
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MATH1111/08Fall/Self-assessment 2 4. Vector spaces (a) What’s the definition? Could you give some examples?
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