{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Math 54 - Midterm 01 Review, Spring 2006 (2)

# Math 54 - Midterm 01 Review, Spring 2006 (2) - MATH 54...

This preview shows pages 1–2. Sign up to view the full content.

MATH 54 Midterm 1 Review Edward Carter February 13, 2006 1 Linear Equations and Matri- ces 1.1 Things to Know How to row-reduce a matrix, and how to read the solution set of a linear system from its row- reduced matrix. If A is m × n and B is n × q , then C = AB is m × q , and C ij = n k =1 A ik B kj . In general AB 6 = BA . However, A ( BC ) = ( AB ) C , and A ( B + C ) = AB + AC . If A is a square matrix, then the inverse A - 1 is a matrix such that A - 1 A = AA - 1 = I , if such a matrix exists. In this case, A is called invertible. The inverse of a matrix A is unique if it exists. If A and B are both invertible, so is AB , and ( AB ) - 1 = B - 1 A - 1 . How to compute inverses via row-reduction. The three types of elementary matrices. Let A be an n × n matrix. Then the following are equivalent: A is invertible. AX = B has a unique solution for any B . AX

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Math 54 - Midterm 01 Review, Spring 2006 (2) - MATH 54...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online