![SOLVED:(10 marks) Suppose A is an n X n real matrix. Show that A can be written sum of two invertible matrices. HINT: for any A € R_ we can write A = SOLVED:(10 marks) Suppose A is an n X n real matrix. Show that A can be written sum of two invertible matrices. HINT: for any A € R_ we can write A =](https://cdn.numerade.com/ask_images/9b94775e7d7649e1840b510aee49fdbd.jpg)
SOLVED:(10 marks) Suppose A is an n X n real matrix. Show that A can be written sum of two invertible matrices. HINT: for any A € R_ we can write A =
![SOLVED:Show that all matrices similar to an invertible matrix are invertible. More generally, show that similar matrices have the same rank. SOLVED:Show that all matrices similar to an invertible matrix are invertible. More generally, show that similar matrices have the same rank.](https://cdn.numerade.com/previews/8553257c-46a3-4d4d-8477-b442e0ea3f25_large.jpg)
SOLVED:Show that all matrices similar to an invertible matrix are invertible. More generally, show that similar matrices have the same rank.
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![SOLVED:Show that if the matrix B is invertible then the only solution of the equation BX = 0 (where 0 is the zero square matrix Of the same size as B) isX = SOLVED:Show that if the matrix B is invertible then the only solution of the equation BX = 0 (where 0 is the zero square matrix Of the same size as B) isX =](https://cdn.numerade.com/ask_images/217b703633d648c7abaa2dc8f692c80a.jpg)