MA122 Study Guide - Midterm Guide: Codomain
MA122 Mock Midterm
Answers
(Full Solutions will NOT be posted;
use the MAC’s drop-in help centre if you have any questions.)
**** Please remember that the mock test was meant as a means of providing an extra set of practice
questions and basis for a review class. Do not study for the midterm based solely on the topics covered by
the mock test! Go back through notes/labs/homework to ensure you have reviewed all concepts discussed
in the course.
1. 2
6
4
2 0 1
3 1 1
22 0
3
7
52. — — – !use properties of transpose to show
(kB C)T= =(kB C))
3. Ais a subspace of R44. (a) 9
p902 (b) p821
5. — — – !use !
v1(k1!
v1+k2!
v2+k3!
v3) = !
v1!
0to show that k1= 0
!similarily, show that k2= 0 and k3= 0
6. — — – !use property that k!
uk2=!
u!
uto show LS = =RS
7. (a) 4
p21 (b) 3x3y+ 6z=27 (or any multiple, such as x+y2z= 9)
(c) the line is parallel to the plane 0
8. (a) — — – !show the rank of the
corresponding matrix
would be 4
(b) !
v=1
3
2
6
6
6
6
6
4
3
0
3
6
3
7
7
7
7
7
5
+ 2
2
6
6
6
6
6
4
0
2
3
1
3
7
7
7
7
7
5
+
2
6
6
6
6
6
4
0
2
2
0
3
7
7
7
7
7
5
9. (a) a= 2 (b) a=2(c) a2R,a6=2(justify each answer!)
10. (a) !
x=
2
6
6
6
6
6
6
6
4
13s2t
1 + st
s
t
t
3
7
7
7
7
7
7
7
5
=
2
6
6
6
6
6
6
6
4
1
1
0
0
0
3
7
7
7
7
7
7
7
5
+s
2
6
6
6
6
6
6
6
4
3
1
1
0
0
3
7
7
7
7
7
7
7
5
+t
2
6
6
6
6
6
6
6
4
2
1
0
1
1
3
7
7
7
7
7
7
7
5
,s; t 2R
(b) for ex: if s= 0 = tthen a sol’n would be !
x= (1;1;0;0;0)
if s= 1 and t= 2 then a sol’n would be !
x= (8;0;1;2;2)
11. (a) Domain = R4Codomain = R3(b) (i)
2
6
6
4
1
0
7
3
7
7
5(ii) unde…ned
12. — — !show that S(k~v +~u) = kS (~v) + S(~u)for any k2R,~u; ~v 2R3
Document Summary
Answers (full solutions will not be posted; use the mac(cid:146)s drop-in help centre if you have any questions. ) **** please remember that the mock test was meant as a means of providing an extra set of practice questions and basis for a review class. Do not study for the midterm based solely on the topics covered by the mock test! Go back through notes/labs/homework to ensure you have reviewed all concepts discussed in the course: 264. 4p21 (c) the line is parallel to the plane (cid:25)0: (a) (cid:151) (cid:151) (cid:150) ! show the rank of the corresponding matrix would be 4 (b) (cid:0)!v = 3777775: (a) a = 2 (b) a = (cid:0)2 (justify each answer!, (a) (cid:0)!x = , s; t 2 r (cid:0)1 (cid:0) 3s (cid:0) 2t. 1 + s (cid:0) t s t t. 266666664 (c) a 2 r, a 6= (cid:6)2 (cid:0)2 (cid:0)1.
