{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Math 3013 Quiz 3 Solutions

# Math 3013 Quiz 3 Solutions - Math 3013 Linear Algebra Fall...

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

Math 3013 Linear Algebra, Fall 2012 Quiz 3 Oct. 10, 2012 1. Determine if the following matrix is invertible or not. If it is invertible, ﬁnd its inverse. A = 1 - 1 - 2 2 - 3 - 5 - 1 3 5 Solution ± A I ² = 1 - 1 - 2 1 0 0 2 - 3 - 5 0 1 0 - 1 3 5 0 0 1 r 2+ r 3 -→ 1 - 1 - 2 1 0 0 1 0 0 0 1 1 - 1 3 5 0 0 1 r 1 r 2 1 0 0 0 1 1 1 - 1 - 2 1 0 0 - 1 3 5 0 0 1 r 2 - r 1 ,r 3+ r 1 1 0 0 0 1 1 0 - 1 - 2 1 - 1 - 1 0 3 5 0 1 2 ( - 1) × r 2 1 0 0 0 1 1 0 1 2 - 1 1 1 0 3 5 0 1 2 r 3 - 3 r 2 1 0 0 0 1 1 0 1 2 - 1 1 1 0 0 - 1 3 - 2 - 1 ( - 1) × r 3 1 0 0 0 1 1 0 1 2 - 1 1 1 0 0 1 - 3 2 1 r 2 - 2 r 3 1 0 0 0 1 1 0 1 0 5 - 3 - 1 0 0 1 - 3 2 1 2. Compute the LU factorization of A = 2 - 1 0 0 6 - 4 5 - 3 8 - 4 1 0 4 - 1 0 7 Solution A = LU can be written into 2 - 1 0 0 6 - 4 5 - 3 8 - 4 1 0 4 - 1 0 7 = 1 0 0 0 * 1 0 0 * * 1 0 * * * 1 * * * * 0 * * * 0 0 * * 0 0 0 * 1. The ﬁrst row of U . By using matrix multiplication and the ﬁrst row of A , we have 2 - 1 0 0 6 - 4 5 - 3 8 - 4 1 0 4 - 1 0 7 = 1 0 0 0 *

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 3013 Quiz 3 Solutions - Math 3013 Linear Algebra Fall...

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

View Full Document
Ask a homework question - tutors are online
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}