Download Math 4R - Farmingdale School District

Math 4R
Linear Systems & Matrices HOMEWORK
HW # 47: lJIJe el,i8lMeltliis
p.
p.
p.
p.
528
529
540
542
I:u:
'iI
18 II !f!la2
- # §7, 60
- # 64
- # 39 - 42
- # 72. 74 (word DFoblems)
HW#48:
WS - Practice Worksheet 2-1
HW#49:
-2
I. Given the matrix
A =
[0
53 -13]
list the elements indicated below:
II. Write a matrix whose elements are b11
b31 2, b32 7.
What are the dimensions of matrix B?
=
=
= 2, b = -3, b = 1, b = -5,
12
21
22
III. Solve the system of equations:
3x+4y = 375
5x+2y = 345
IV. For each of the following systems of equations:
(i)
Label as consistent or inconsistent, dependent or independent.
(ii)
Solve algebraically (use any method you wish).
(a)
(c)
y = 2x+3
y-x=l
(b)
y-x = 1
x-y=2
2y+3x=6
2x+2y = 6
(d)
y=-x+3
3
y=--x+l
2
V. Solve the matrix equations:
(a)
[x
2y] = [y +
5
x-
3]
(c)
[X y-1
1]
=
[Y -
x+
x+l
1]
HW#SO:
I. p. 615 -
#
5,7,9
II. The equations
3x + 2y = 7
and
kx + 6y = 8 are inconsistent. Find k.
III. Solve the following matrix equation:
1 [- x_ -1 3] = [-21]
2x
[y + 2 +
I.p.615-#15-19
Using your results to parts (a) and (b) to justify your answer, is matrix
multiplication commutative?
II. Study for Quiz
HW#S2:
WS - Practice Worksheet 2-2
Study for Quiz
Quiz!!
HW#S3:
WS - Laboratory 9: Matrix Algebra -
#
1 - 6, 8, 9, 11
HW#S4:
I. Find the value of each determinant.
-3
(a)
I1
(c)
7 16
13
8
II. Text p. 635 -
_541
#
(b)
5
8
1_ 3 -2
4
(d)
[-0
8
2
41 - 44, # 57,58
III. Vera Clean starts a Garpet cleaning business and buys a carpet cleaning maohine for
$500. It costs her $10 per carpet for ohemioals and other expenses and she oharges
$12 per carpet for cleaning.
(a) 'IVflatis her fixed Gost? l=Ier vaFiae.'<) Gost?
(b) If she cleans 120 oarpets does she make a profit or loss? 1=10'11 much?
(0) If she cleans 280 carpets does she make a profit or loss? I=IO'A' ffiuoh?
(d) l=IO'tvmany does she need to olean in order to break even?
(e) l=Iow maR'y does she need to olean in order to make a $200 profit?
HW# 55:
Text p. 625 -
#
10 - 16
{Find the inverse of each matrix}
HW# 56:
Text p. 626 -
#
39, 45, 47, 49
HW#57:
WS - More Solving Matrix Equations
Study for Quiz.
HW# 58:
p. 615 - # 2,11,21,23
p. 626 - # 40, 50
p. 634 p. 650 -
#
#
7, 12
45, 46
WS - Cramer's Rule - # 3 - 6
Study for Test!!!
I~
I ~.. I
NAME
- -l1:.:LJ Pradice
Solvin,$JIsteMs
t!)f
DATE
Worksheet.
e._ions
St.te whIJIltsr- each SJl,hm i"CDuistent snd independent,
cona/st8nt and tlelJsndsnt. or inconsi8tent.
1.
ax + 4y :::5
2x - 5y
.
2. 3x -:-3y ;: 12
-x + y = - 4
=8
Solve·each system by (pSIphing.
8. 3x - y ::: 6
4. 2x + 3y = 12
x+y=6
x+y=6
y
0
y
)(
0
If
Solve esch sy.sMm of equations BlgebraiCIIlly.
5.
ax - 2y :; 7
6. 4x ~ 3y = 15
x+y=4
2x+y=5
7. 3x + 4y = 8
-3x - 4y = 10
8. 2x - y ~ 6
x+y=6
9. 3x - 2y =-9
4x + 5y = 11
10. 7x - y; 9
2x + 3y =:; 19
7
GI8nc:oe Division, Maanlllan/McGraw-H~!
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u
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q
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DA fE
\l'iJ-\lVIr.
Practice Worksheet
Introduction to Matrices
Use matrices A, B, and C to find each sum, difference, or product.
A=
2-1 31 41J
l
5 -2
3
B=
l-1
5 6J
2 -7 -2
4 4 2
C = [8
10 -9J
12 14
-6
1. A +B
2. A - B
3. B-A
4. -2A
5•
6.AA
AD
£1U
7. CA
8. CB
9. (CE)A
10. C(BA)
Find the v'1lues of x and y for which each matrix equation is true.
11.
[2x4~3] = [3~J
12.
[n
=
8
Glencoe Division, Macmillan/McGraw-Hili
[2Y2~ 4]
Laboratory 9 Exercises: Matrix Algebra
,~,--~.~,.
IfA=[~ -2
D=
[-10]
2
4
!]
B
=
[3 0 -1]
C = [0 4 5]
E
=
[-2 0 3]
F
3
2
-1
0
4
5
-1
-1
2
4
6
5
1
=
[2 3]
4
5
0
-1
find:
1.A +F
2. E-B
3.D·C
4.C·D
5. B·E
6. A-[
7. B· B-1
8. F-A
9. C·F
10. E-1
11. 2F - 3A
[ = [~ ~]
Matrices Practice 1
Perform the indicated operation, whenever possible.
1.
[-1 1] [6 2] =
2
+
5
6-3
4.[8 -7]+[-6 4]_[-4 -7]
-7
5
7
8x-7y
5. I
-2
=
4-9
5x-5y
-3k-8z
8w-5v
-
-4m+5n
8k-3z
5w+9v
6m-7n
Find the indicated expression.
6. Let A
=
[1 3]
2 5
and B
=
[0 4] . .
-1
6
Find 3A + B .
{OVER}
7. Let
C=[~3] D=[~J
and
Find
C-4D.
Perform the matrix multiplication.
8.
[-1 3][-2 0]=
3
11.
2 -1
2
[-8 3
-7 9
{OVER}
Evaluate each determinant.
12. 1-2
1
41
3=
102
13.1-3 1 -2
421
-2
1
5
2
-1
-1
4
1
-1
-1
-4
2
2
2
14.13
o
231
15.10
16 16 -3
. '1
3'
-4 5
=
F3
'i~
f.
J;;actice Worksheet------
:'"-~
I:.
t,
•
DATE ----
Determinants and Multiplic ....tive In\~'er~;esof a Matrix
Find the value of each determinant .
1.
2 -1
3.
. I '3 -1>1
1 9
I_~ ~I
2
-3
~,'
c~
31
1
41
iJl:,
1
1 -2
-1
1
I '2..
-:1
.5
Find the inverse of each matrix if it exists.
1
5. [ 5
21
6, [
•
.::/
oj
S. 2x: -
ay
Solve each system by using matrix equations .
7. 3x + Y = 23
2x + y = 18
=
17
3x + y =: 9
+ 4y = 6
2x - 21y = 21
9. 2x + 5y = ~8
3x - 2y = -15
,
361
-1
10 4
10" 3x
~'
.
;.
<>
U:. 7x - 3y = 4
x + 2y = -14
11. 4x - 3y c.:.:: -16
2x + 5y = 18
!f:
•
9
Glencoe Division, Macmillan/l'v'l.:Gr.,w H II
if')
More Solving Matrix Equations.
'
Solve the following systems of equations using matrix equations.
1.
2.
4x+2y=10
x - Y = 13
2x+3y=7
x+4y=6
{OVER}
..
3.
4.
2x+2y=-6
5x-5y=-15
- 5x- 5y
=
25
- 2x - 4y
= 16
17
Cramer's Rule
Solve each system of equations using Cramer's Rule.
4x-7y =-2
2. x+2y= 7
3x+5y = 7
1. 6x- y=-8
3x+3y =-9
3. -2x+ y=-4
2x+ y+3z =8
4, x+2y-2z
=3
5x+ y+z= 1
x+2y+z
=3
5. 2x+ y-2z
=-4
-x+4y+z=-7
x+3y-2z
=-2
7. -2x-4y+5z
=9
4x + 7y + 10z = 0
2x- y+z=5
9. x+2y-2z=0
- 5x + 3y + 6z = -7
x+ y+2z:=:2
6x+3y-2z
=
1
6. 4x - 2y + 3z = 7
2x+ y-4z=-3
x-2y-3z=-8
8. 2x+4y-z
= -21
5x + 3y + 2z = 14
x+2y+3z
=6
10. 2x - 4Y + 2z = 16
3x+ y-z=-2
2x- y+z=6
11. 2x - y + 3z = 5
12. x + 3y+5z = 10
x-y-z=-2
4x-4y+2z=
-3
Matrix Review
Use matrices D, E, F, and G to complete # 1 - 3.
3
D=[ -6 ~] E=r
_19
4
q
F=
[-62 -/ :4]
-3
3. EF
2. 3E - G
1. -2D
Find the value of each.
3 -2
8 -9
4.13
10
6. Find the inverse of
5
5.17
1
-4
o
1
1
[3 -6]
1 _ 2 ,if it exists.
:ylJ
Y
7. Find the values of x and y for which
3
r
=
rX+5l
1~ J is true.
Solve each using matrix equations.
8. 4x - 3y ;:: 2
7x + y 6
=
10. Solve using Cramer's Rule.
9. 2x - 3y =-8
-3x + 5y 13
=
x - 3y - 3z ;:: 0
2x + 5y - 5z = 1
-x + 5y - 6z = -9
G=
r 3 -4
5
2
-8
6
J
Matrix Review II
Use matrices A, B & C to complete #1-4.
A
=
l2-1
OJ
2
1) -4A
3) Be
4) BC-2A
Find the value of each determinant for #5 & 6.
2 -1
5) 14
6)
6
l
3x+2y =2
4x+ y=-4
2 4
6
3
-3
7) Find the values of x & y for which X+8
3
8) Solve
-1
x+ y+2z=2
2x - y + 3z = 5
x-y-z=-2
7 0
-5J = l38 -5
-y
using matrix equations.
9) Solve using Cramer's Rule:
5
.
3
4y-1O
J is true.