Math 110 - Fall 2002 - Geba - Midterm 1

Math 110 - Fall 2002 - Geba - Midterm 1 - 1

• Test Prep
• 1
• 100% (1) 1 out of 1 people found this document helpful

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 05/12/2003 MON 15:45 FAX 6434330 MOFFITT LIBRARY I001 MAT 110 — MIDTERM 9/27/0Jt D'Gelibfb 1. Let T : R3 —> R2 the linear transformation deﬁned by T(x,y,2) = (\$+y+z,\$+3y+5z). a) Find N (T), R(T) and compute dim N (T), dim R(T). b) Let ,8 and 7 the standard bases for R3 and R2 respectively. Consider also 0: — {(1, 1, 1), (2,3,4), (3, 4, 6)} basis for R3. Compute Q the change of coordinate matrix from ﬂ to at and the represen— tation matrices [T]g,[T]g. Check that mrc=nn 2. Let V and W two vector spaces over the rational numbers ﬁeld Q and T : V —> W which satisﬁes T(m+y) = T(:c) + T(y). Prove that T is a linear transformation. 3. Let m and 71 two positive integers. Construct a linear transformation T such that nullity(T) : m and rank(T) : n. 4. Let T : V % V a linear transformation, Where V is a ﬁnite—dimensional vector space. Prove that if r'ank(T):rank(T2) then R(T) ﬂ N(T) : {O}. 5. Let A,B two square matrices, A,B E Jllnxn(R) such that In 7 AB is invertible. Prove that In — BA is invertible. ...
View Full Document

• Fall '08
• GUREVITCH

{[ 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