Midterm 1-33A 2007 Summer

Midterm 1-33A 2007 Summer - englishMATl-I 33A LECTURE 1 1ST...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

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.

Unformatted text preview: englishMATl-I 33A LECTURE 1 1ST MIDTERM 2 Problem 1. (True / False, 2 pts each) Mark your answers by ﬁlling in the appropriate box next to each question. The matrix 001—1 1 O is in reduced row echelon form. 1 x wowo :3 There are no two 2 matrices A and B for which AB = BA. 1 7 6 i If the matrix of a linear transformation T is 14 20 3 ] , then 11 22 9 21m: (iv: IE) There is a 3 x 4 matrix A with kerA = {0}. " I) A 3 x 3 invertible matrix always has rank 3. If A is an invertible 3 x 3 matrix, then the image of A is spanned by the vectors (v1 1 O 0 0 , 1 , 0 0 O 1 1 1 0 . 2 v. Thevectors[1],[0],[1]areaba51sfor1§. ‘ F D The vectors 1 , 1 and 0 s an R2. 1 0 1 p I) No s stem of linear e nations can have exactl two (i.e., two and onl two) distinct Y Cl Y Y solutions. ; 2 33 If V and W are two subspaces of R”, then dim(V + W) s dim V + dim W. .i MMMMMMMMMM MMMMM NE 3.” 3 my mat m My. ,1. M [01. x M i. §§§i§§§é m M MMMMM MM M M m1... Q we 33% . 5 é, a? w M! _ _ we ﬁgmy wétzgézw mi «6% 1 1 1 4% mm, @3wa M3,? .3} \$303; «8 :2. Waavﬁéagzgasﬁimw My 5. £633 5% MW” 3mg» ﬁg :2 __ i : MMMMM WM MMmM MM : AMMMMMMMMM MW MM MM MM MM M k \w “A. M: Mm MMM ,,,,, 23% a MM MMMMMM Q 5% MM MMMMMMMMM ﬁt is Mg 1ST MIDTERM ,, 4 579 7009 456 ,englishMATH 33AMLECTURE 1 Find a basis % for the image and %’ for the kernel of A. (b) Let 12 ”M me (where Q3 is your basis for the image from part (a)). Problem 2. (20 pts) (a) Let g (4%? MMMKRM eng11§hMAIH 33A LECTURE: , V 157T MDTFRM ,_ Problem 3. (20 pts) Let T : R3 ——> R3 be rotation by 30" about the at—axis, counterclockwise as Viewed from the positive :1: axis. (a) Find the matrix [T]. (b) Find a nonzero integer k for which [Tyc z I. .3“. 5 51% g‘i‘x g“ (gigmtﬁﬁ or \$1; lady? mew FM: «up-’32 5m 4 englishMATHBBA LECTURE 1 , H: JET MIDTERM 5 Problem 4. (20 pts) Let E be the line in R2 given by the equation 3/ =, 3:5. Let T be the reﬂection about 3 and P be the projection onto E. (a) Find the matrices [T] and [P]. (b) » Compute {H2007 and [TF7 (Hint: 27 is odd). AWN 43:; mg: 2;: , j MM; 1 Ma 75 '° 7 [m :2 a ~ g . c, _ “i- ; q «a W. s ”1:?" ﬂ »' :2: :13 3' Jezeeéaeswia 3:2 mfg: g, {73 5% a}? :33: f a 5: ti; 3} ye} i f ”Mia? M g r ‘9 r?“ 3;; W a“ ~ W e a} w a»: "i W M ewe :Q Q; «, . 3 ~ if \$55 7 g; i 59%: if”: Kg “g“ Kiwi ; LE: 4‘3“}.w gem ; (L: pét : “x Egg; its?» M} 4:? x M EB g , W a w we, a ( ,englishMATH 33A LECTURE1,,__ ,_,1ST,_MIDTERM_ ,, _, 6,__,, , , , Problem 5. (20 pts) Let A be an invertible n x n matrix, and let B be an n x m matrix. (a) Show that ker AB = ker B. (b) Express the rank of AB in terms of the rank of B. f“ a 3: 3‘ ﬂ 3 E W,“ fl“, m r {ASE {igieewzk ”Birgit: 35 a, *3 iii a. \$3511 3???" gig M if} 3 W {is r33; at 3%i’9é’g {:32} l :2 WE W ﬁtiéivga‘ ﬁaggx \$3) ...
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