This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: UCLA Math 33A Lec 2, Winter 2008 Midterm 1 Feb 1, 2008 Last name: First and middles Names: g g w _ UCLA ID number: Section (circle one): 2A WONG, WANSHUN Tuesday
23 WONG, WANSHUN Thursday
20 KWON, SOONSIK Tuesday
213 KWON, SOONSIK Thursday Instructions: 0 FEB in your name ané circle your section above.
a You are allowed to use your brain, pencii/ pen, eraser oniy.  You can use the blank pages if you need space to ﬁnish your solution. Please indicate cleariy
Where it may be found. a Show ah the necessary steps involved in ﬁnding you: solutions1 except True~False questions. Problem 1: (10 pts) Indicate Whether each statement is true or false (circle your answer, and
you need not justify your answer here). 1. 10. . There exists a 2 X 2 matrix A such that A m and A m . T 2 “ w 2 _ The function T m Gym? 2) (y 2) > is a linear transformation. K F . The matrix ( 1 3 0 1 ‘ Matrix 0 0 1 2 is in rref. F
0 O O O . If 11'} 'LU ere nonzero vectors in R3, then iii must be a linear combination of if and 17.
T {F . if A 4 X then there exists a vector 3 E R4 such that the system A5 = I; is
inconsistent. T F (A) < : (Ali—i), then the system of linear equations Af = Ernest be inconsistent. . If A is e 3 x 4 matrix of rank 3, then the system A55 = 2 1
must have inﬁniteiy many
3
solutions. (SE W4)? —— (m~i~4)2 IfAendBaretwoéiXBm 'es such that A6 = B??? for all vectors 1? E R3, then matrices
A and B must be equal. " _6 5) represts a rotation combined with a scaling. The formula det(2A) m 2 det(A) holds for ail 2 X 2 matrix A. T ) ‘ I. (6 pés) Find the inverse of A. 221 010 230 Probiem 2: Let A = ( Problem 3: 1. (6 pts) Find a nonzero 2 x 2 matrix A such that Af is peraiiei to the vector (1) , for ali 1i? 6 R2. Find the inverse if exists. 2. (7 pts) Find the 3 x 3 matrix of the reﬂection in R3 about the inane y w 2. Find the inverse
if exists. 3. (7 pts) Find the 2 X 2 matrix of the iinear transformation that rotates ail vector E E R2 by
120° in the countezciockwise direction, then dilates the resulting vector by a factor of Find
the inverse if exists. Problem 4: (8 pts) Does there exist an invertible matrix that has a column of all zeros? If so then ﬁnd one, if not then expiain why not. wiil be given for right answer but wrong reason.) ...
View
Full Document
 Spring '08
 lee
 Math

Click to edit the document details