Midterm 1-33A 2007 Summer

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

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

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
Image of page 5
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

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern