In order to put Miss Loi’s new found freedom into good use, it’s about time the Matrix is loaded onto this website … hohoho.
Do take particular note on the second question of Part 1. Recently Miss Loi’s been seeing that more and more school papers are testing students’ understanding of concepts like these (which is the right thing to do).
From experience, many students don’t pay enough attention to mundane little things like the conditions for inverses to exist. Even Miss Loi is sometimes guilty of that in her uni days :P.
- Given that A =
![delim{[}{matrix{2}{3}{{-2} 2 3 1 {-1} 0}}{]}](https://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_971.5_80a4141459dac36039b6393e9f1d0dd9.png "delim{[}{matrix{2}{3}{{-2} 2 3 1 {-1} 0}}{]}")
![delim{[}{matrix{2}{3}{{-2} 2 3 1 {-1} 0}}{]}](data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20viewBox=%220%200%20210%20140%22%3E%3C/svg%3E "delim{[}{matrix{2}{3}{{-2} 2 3 1 {-1} 0}}{]}")
and B = , find AB.
State, with reason, whether A-1 and (AB)-1 exist. - Given that M =
![delim{[}{matrix{2}{2}{4 5 2 3}}{]}](https://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_971.5_891051251d3e490a27f63028e129663e.png "delim{[}{matrix{2}{2}{4 5 2 3}}{]}")
, find the matrix N such that MN = NM.
![delim{[}{matrix{3}{2}{3 {-4} 1 2 {-1} 1}}{]}](https://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_956.5_19a6b224540367bb3684e7b89ca3b667.png "delim{[}{matrix{3}{2}{3 {-4} 1 2 {-1} 1}}{]}")
, find AB.So what would you do Neo?
