lecture_10- Finding Inverses of Matrices Part 2

lecture_10- Finding Inverses of Matrices Part 2 - MA 265...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA 265 LECTURE NOTES: WEDNESDAY, JANUARY 30 Finding Inverses of Matrices (contd) Nonsingularity. Let E = E 1 E 2 E k 1 E k be a product of elementary matrices. Then E is nonsingular. We began the proof of this statement in the previous lecture. It suffices to show that each elementary matrix E i is invertible. Recall that there are three types of elementary matrices corresponding to the three types of elementary row operations. For Type I, say that we wish to interchange row i and row j . To undo this operation, we simply interchange the rows a second time: E = 1 . . . 1 1 1 . . . 1 1 1 . . . 1 = E 1 = 1 . . . 1 1 1 . . . 1 1 1 . . . 1 . (Recall that we constructed E by simply interchanging the i th and j th rows of the n n identity matrix I n .) For Type II, if say that we wish to multiply row i by a nonzero number k . To undo, we simply divide row i by k : E = 1 . . . 1 k 1 . . . 1 = E 1 = 1 . . . 1 1 /k 1 . . . 1 . (Recall that we constructed E by multiplying the i th row of the n n identity matrix I n by k .) For Type III, say that we wish to add a multiple of row j to row i . To undo, we simply subtract the same multiple of 1 2 MA 265 LECTURE NOTES: WEDNESDAY, JANUARY 30 row j from row i : E = 1 ....
View Full Document

This note was uploaded on 02/25/2010 for the course MA 00265 taught by Professor ... during the Spring '10 term at Purdue University Calumet.

Page1 / 4

lecture_10- Finding Inverses of Matrices Part 2 - MA 265...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online