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MATH1115 ASSIGNMENT

创建日期：2024-05-22 16:35:41

所属分类：数学mathematics

标签： MATH1115

ASSIGNMENT

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MATH1115 ASSIGNMENT

DUE MONDAY MARCH 27 AT 11PM
Homework Policy
The following rules apply to collaboration and the use of outside resources:
• Collaboration with other students is allowed – encouraged, in fact – but if
you collaborate with other students you must acknowledge the collaboration
in writing at the top of your assignment. For example, “On problems 1
and 4 I benefitted from conversations with John Doe, and my solution to
problem 5 was obtained in collaboration with Jane Doe.” Assignments
without a collaboration statement will not be graded.
• The use of outside resources is also permitted, but be careful. For example,
you are allowed to read about Venn diagrams on Wikipedia. You are not
allowed to read the solution to an assignment problem someone posted on
Stackexchange. If in doubt, ask before you look. Any such use must also
be acknowledged in writing in the assignment.
• Unless otherwise noted, the problems should be solved without the assis-
tance of computer software.
• Regardless of which sources you use, the writing of all solutions must be
your own.
Note that this is only half of the assignment. The other half is a MATLAB
Grader assignment.
(0) (a) Write a collaboration statement, detailing who you worked with and
any outside resources you may have used. (You don’t need to mention
help you received from the lecturers, your demonstrator, or the drop-in
centre.) This part is mandatory.
(b) Write a reflection on how the course is going. Did you go to lectures,
and to your workshop? Did you spend time with a study group, or use
any of the other resources (like the drop-in centre or office hours) that
are available to you? How much time did you spend on the course in
the past week? This part is optional.
(1) (4 points) Suppose that A,B are non-empty subsets of R. Show that if
A ⊂ B and B is bounded from above, then supA exists and supA ≤ supB.
(2) (7 points)
(a) (3 points) Let f : R → R be a function which is continuous at x = 0.
Use the definition of differentiability to prove that the function g :
R → R defined by g(x) = x(f(x)) is differentiable at x = 0 and find
g′(0).
1
2 MATH1115 ASSIGNMENT 5, DUE MONDAY MARCH 27 AT 11PM
(b) (4 points) Again using the definition of the derivative, calculate the
derivative of f(x) = 12+5x on its natural domain (−∞,− 25 )∪(− 25 ,∞) =
R\{− 25}. You may not use any differentiation rules (like the product
rule, the quotient rule, etc).
(3) (4 points) The final calculus question will be posted after the Modelling
Workshop on Thursday, 23/3.
(4) (3 points) Without computing any inverse matrices, solve the following
equation for X:
X ·

2 5 1 3
42 11 −165 13
6 13 −12 22
7 17 6 5
 =

2 5 1 3
42 11 −165 13
8 18 −11 25
1 2 3 −4

(5) (Total of 8 points) Recall that the transpose AT of a matrix is defined by
interchanging the rows and columns: (AT )ij = Aji.
We say a square matrix A is skew symmetric if AT = −A.
(a) (2 points) Show that whenever AB is defined, BTAT is also defined
and (AB)T = BTAT . (For this part A and B do not have to be skew
symmetric.)
(b) (3 point) If A =
 b cf
 is a skew symmetric 3 × 3 matrix, what
are the remaining entries of A? Is A invertible? (Your answer may
depend on b, c and f .)
(c) (3 points) Show that if A is skew symmetric and invertible then A−1
is also skew symmetric. (To be clear: A is not the 3 × 3 matrix from
part (b) but rather a skew symmetric matrix of arbitrary dimension.)
(6) (4 points) Prove that there is exactly one degree at most 2 polynomial
p(x) = a0+a1x+a2x
2 passing through 3 points (x1, y1), (x2, y2) and (x3, y3)
as long as x1, x2 and x3 are distinct. (You may now use determinants if
you want to.)

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239 QF5203 INFR08010 IT114105 FIT2093 ECON3124 ECON1195 MATH 337 STAT 3006 COMP202 COMP3130 MATH3609 COMP 250 CS6140 IEEE ELE00041I FIN40090 CIV 5899 MATH3066 IGNMENT MATH 2009 STAT3405 HIST 101 MATH 3281 CEGE0042 ICT532 LAB 7 LAB 5 MCO455 CSIT214 Q4 IFB104 A1 ECO220Y5Y DA5020 CMPSC473 FIN9007 DSCI553 MSCI534 COMP3308 CSE-112 CMPT 310 EE104 F 2C P20 ALY2010 BUSM060 STA258 ECO00030M R BIOSTAT 274 COS6012-B FIT3155 CMPUT 340 EC421 INFS4205 ECOM135 NATS 1740 COMP809 MBE 6005 STA465 CSSE2310 CIVL2700 DATA4700 CMPSC 473 ISE 529 CS5044 MAST30020 COMP2207 ENGG1001 COMP0046 FIT3165 STAT GR5241 MECH0007 vATHK1001 ANALYTIC ATHK1001 MATH352001 HW3 S1 BMAN 24662 COMP 636 Stat-461 STAT 302 STAT 2132 STAR534 ENG4137 CMP3752M CS3103 BISM3222 STA 135 ME155A IIMT3601 ECON3371 ECON 3371 HW4 FINA 5840 DT211C CTEC3902 MAT005 MATH2148 S261F Econ 332 MATH3734 MIS41270 7CCMFM13 SYST 664 CIS434 CENG10014 MT4111 MT4527 ECMM424 CMT219 Math 136 MATH 3120 COMP10002 MAST20009 MATH0058 BEEM117 ISYE 6420 MGMTMFE 405 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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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