{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

101st_tut1

# 101st_tut1 - (iii If A is a square matrix such that A 2 ±...

This preview shows page 1. Sign up to view the full content.

MATH1111/2010-11/ Tutorial I 1 MATH1111 Tutorial I 1. Consider the system 8 < : x 1 x 2 + x 3 x 4 + x 5 = 1 x 2 x 4 x 5 = 1 x 3 2 x 4 + 3 x 5 = 2 : Determine with explanation whether the following is true. (a) There are two free variables. (b) The free variables must be x 4 and x 5 . 2. This question concerns how to prove or disprove a statement. We start with "common sense". For statments (a) and (b) below, think about what you need to do if you want to prove it. Also, think about how you can disprove it. (a) All apples are sweet. (b) Some apples are sweet. Prove or disprove the following. (i) All matrices X satisfying X 2 = 0 are zero matrices. (ii) Some square matrices B satisfying B 2 I = 0 are singular.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (iii) If A is a square matrix such that A 2 ± I = 0, then there exists a nonzero vector x such that Ax = x or Ax = ± x . 3. Prove or disprove the following. (a) ( A + B ) 2 = A 2 + 2 AB + B 2 for any two n ² n matrices. (b) If A and B are nonsingular n ² n matrices, then A + B is nonsingular. (c) Let A be a nonzero matrix. If AB = AC , then B = C . (d) Let A be invertible such that I + A is invertible. Then ( I + A ) ± 1 = I + A ± 1 . 4. To those "false" parts in Qn 3, ±gure out some conditions such that they become valid statements under the additional conditions....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern