Linear Algebra in Twenty Five Lectures
Tom Denton and Andrew Waldron March 9, 2010
1 What is Linear Algebra? 6 2 Gaussian Elimination 10 2.1 Notation for Linear Systems . . . . . . . . . . . . . . . . . . . 10 2.2 Reduced Row Echelon Form . . .
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Solutions to Practice Midterm 02
March 01, 2012
Student ID Number:
Read each problem carefully.
Write each step of your reasoning clearly.
The best strategy is to solve the easiest problem rst, the second easiest problem
next, etc., work
Preparation I for Midterm 02
March 02, 2012
Problem 01 (5 points) Define what it means for an m n matrix A to be nonsingular .
Problem 02 (20 points) Let A and B both be n n matrices and suppose that the matrix
A is nonsingular and the matrix B i
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(Partial) Solutions to Homework 4 Problem 10.1: Let M be a square matrix. Explain why the following statements are equivalent: i. M X = V has a unique solution for every column vector V . ii. M is non-singular. (Show that (i) (ii) and (ii) (i).) Answer: A
(Partial) Solutions to Homework 3 Problem 7.1: Show that the pair of conditions: L(u + v ) = L(u) + L(v ) L(cv ) = cL(v )
is equivalent to the single condition: L(ru + sv ) = rL(u) + sL(v ) Your answer should have two parts. Show that (1, 2) = (3) and the
(Partial) Solutions to Homework 2 Problem 4.1 Write down examples of augmented matrices corresponding to each of the ve types of solution sets for systems of equations with three unknowns. (no solution, one solution, a line of solutions, a plane of soluti