{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW4_solution

# HW4_solution - Linear Algebra Homework#4 Solution 1 First...

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

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.

Unformatted text preview: Linear Algebra Homework #4 Solution 1. First we want to show that        det  for any elementary matrix E. If E is of type 1, interchanging any row (column) of identity matrix I 2 , then     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1                                                                               Hence we get          det 1  of type 1 elementary matrix. If E is of type 2, then since the rows are fixed, δ is linear.             det k k   for every scalar k . If E is of type 3, let E be obtained from I 2 by adding k times row i of I 2 to j, where j ≠ i, and let A be obtained from I 2 by replacing row j and row i. Then the rows of I 2 , E, and A are identical except for row j. Moreover, row j of E is the sum of row j of I 2 and k times row j of A. Since δ is linear, it follows that                 det 1    k Thus we show that        det  for any elementary matrix E. Secondly we want to show that              . We can consider E is of type 2, multiply a row i k times from I 2 , say           1 k , then                                                                    det 1 22 21 12 11 22 21 12 11 22 21 12 11 a a a a k a a ka ka a a a a k If E is of type 3, say           1 1 m ,                                                                                     ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

HW4_solution - Linear Algebra Homework#4 Solution 1 First...

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

View Full Document
Ask a homework question - tutors are online