Math 4RLinear Systems & Matrices HOMEWORK

HW # 47: lJIJe el,i8lMeltliis I:u: 'iI 18 II !f!la2

p. 528 - # §7, 60p. 529 - # 64p. 540 - # 39 - 42p. 542 - # 72. 74 (word DFoblems)

HW#48:

WS - Practice Worksheet 2-1

HW#49:

[-2

I. Given the matrix A = 0 5 3] list the elements indicated below:3 -1

II. Write a matrix whose elements are b11 = 2, b12 = -3, b21 = 1, b22 = -5,b31 = 2, b32 = 7.What are the dimensions of matrix B?

III. Solve the system of equations:

3x+4y = 375

5x+2y = 345IV. 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) y = 2x+3y-x=l

(b) y-x = 1x-y=2

2x+2y = 6(c)

y=-x+3

2y+3x=6(d) 3

y=--x+l2

V. Solve the matrix equations:

(a) [ x 2y] = [y + 5 x - 3]

(c) [X - 1] = [Y - x + 1]y-1 x+l

HW#SO:

#I. p. 615 - 5,7,9

II. The equations 3x +2y = 7 and kx +6y = 8 are inconsistent. Find k.

[2x 1 [- x - 3] [- 1]III. Solve the following matrix equation: y + 2 + _ 1 = 2

I.p.615-#15-19Using your results to parts (a) and (b) to justify your answer, is matrixmultiplication commutative?

II. Study for Quiz

HW#S2:

WS - Practice Worksheet 2-2Study 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_541 (b) 1_

83

5(a) I 1 -2

7 16(d) [-0

4 8(c) 13 8 2

II. Text p. 635 - # 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=IervaFiae.'<) 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 EquationsStudy for Quiz.

HW# 58:

#p. 615 - 2,11,21,23p. 626 - # 40, 50p. 634 - # 7, 12p. 650 - # 45, 46

WS - Cramer's Rule - # 3 - 6

Study for Test!!!

I ~.. I NAME DATE- -l1:.:LJ Pradice Worksheet.Solvin,$JIsteMs t!)f e._ionsSt.te whIJIltsr- each SJl,hm i"CDuistent snd independent,cona/st8nt and tlelJsndsnt. or inconsi8tent. .1. ax + 4y :::5 2. 3x -:-3y ;: 12

2x - 5y = 8 -x + y = - 4

Solve·each system by (pSIphing.8. 3x - y ::: 6

x+y=64. 2x + 3y = 12

x+y=6y

0 )(

y

0 If

Solve esch sy.sMm of equations BlgebraiCIIlly.

5. ax - 2y :; 7 6. 4x ~ 3y = 15x+y=4 2x+y=5

7. 3x + 4y = 8-3x - 4y = 10

8. 2x - y ~ 6x+y=6

9. 3x - 2y =-94x + 5y = 11

10. 7x - y; 92x + 3y =:; 19

7GI8nc:oe Division, Maanlllan/McGraw-H~!

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~ ~ Practice Worksheet:'f Introduction to Matrices

Use matrices A, B, and C to find each sum, difference, or product.

l2 3 1J l-1 5 6JA = -1 1 4 B = 2 -7 -2 C = [8 10 -9J5 -2 3 4 4 2 -6 12 14

1. A +B 2. A - B

3. B-A 4. -2A

5 AD• £1U 6.AA

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 = [2Y2~ 4]

8Glencoe Division, Macmillan/McGraw-Hili

,~,--~.~,. Laboratory 9 Exercises: Matrix Algebra

IfA=[~ !] [ 3 0 -1] [ = [~ ~]B = 2 5 4 C= [0 4 5]-2 3 -1 -1 6

[-10] [-2 0 3] [2 3]D= 2 E = 0 -1 5 F = 4 04 4 2 1 5 -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 -2 4-9

8x-7y 5x-5y-3k-8z 8k-3z

5. I -8w-5v 5w+9v

-4m+5n 6m-7n

Find the indicated expression.

[1 3] [0 4] .6. Let A = and B = . Find 3A + B .2 5 -1 6

{OVER}

7. Let C=[~3] and D=[~J Find C-4D.

Perform the matrix multiplication.

8. [-1 3][-2 0]=3 2 -1 2

11. [-8 3-7 9

{OVER}

Evaluate each determinant.

12. 1-2 41 3

1 =

102

13.1-3 1 -2421

-2 1 514.13 2 -1

o -1 4

231

15.10 1 -1-1 -4 2

2 2

16 16 -3. '1 3' =-4 5

F3

f. :'"-~ J;;actice Worksheet------ DATE ----

Determinants and Multiplic ....tive In\~'er~;esof a MatrixFind the value of each determinant .

1. I_~ ~I'i~I:.t,•

.::/

,~'

. ;.<>

!f:

•

•

c~ I '3 -1>1~,'.1 9

3.2 -1 312 1 41

-3 1 -2

1 -1iJl:, I '2.. 1

.5 -:1

Find the inverse of each matrix1 if it exists.

5. [ 5 2110 4

6, [ 361-1 oj

Solve each system by using matrix equations .7. 3x + Y = 23 S. 2x: - ay = 17

2x + y = 18 3x + y =: 9

9. 2x + 5y = ~83x - 2y = -15

10" 3x + 4y = 62x - 21y = 21

11. 4x - 3y c.:.:: -162x + 5y = 18

U:. 7x - 3y = 4x + 2y = -14

9Glencoe Division, Macmillan/l'v'l.:Gr.,w H II

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More Solving Matrix Equations.

Solve the following systems of equations using matrix equations.

4x+2y=101.

x - Y = 13

2x+3y=72.

x+4y=6

' ..

{OVER}

2x+2y=-63.

5x-5y=-15

- 5x- 5y = 254.

- 2x - 4y = 16

17

Cramer's Rule

Solve each system of equations using Cramer's Rule.

3x+5y = 71. 6x- y=-8

4x-7y =-22. x+2y= 7

3x+3y =-93. -2x+ y=-4

2x+ y+3z =84, x+2y-2z = 3

5x+ y+z= 1

x+2y+z = 35. 2x+ y-2z =-4

-x+4y+z=-7

6x+3y-2z = 16. 4x - 2y + 3z = 7

2x+ y-4z=-3

x+3y-2z =-27. -2x-4y+5z = 9

4x + 7y + 10z = 0

x-2y-3z=-88. 2x+4y-z = -21

5x +3y +2z = 14

2x- y+z=59. x+2y-2z=0

- 5x +3y +6z = -7

x+2y+3z = 610. 2x - 4Y + 2z = 16

3x+ y-z=-2

x+ y+2z:=:211. 2x - y + 3z = 5

x-y-z=-2

2x- y+z=612. x + 3y+5z = 10

4x-4y+2z= -3

Matrix Review

Use matrices D, E, F, and G to complete # 1 - 3.

D=[ -63 ~] E=r _19 q F = [-62 -/ :4] r 3 -4J

G= 5 2

4 -3 -8 6

1. -2D 2. 3E - G 3. EF

Find the value of each.

8 -94.13 10

3 -2 55.17 1 -4

o 1 1

[3 -6]6. Find the inverse of 1 _ 2 ,if it exists.

r3Y l rX+5l

7. Find the values of x and y for which :yJ = 1~ J is true.

Solve each using matrix equations.

8. 4x - 3y ;::27x + y = 6

9. 2x - 3y =-8-3x + 5y = 13

10. Solve using Cramer's Rule. x - 3y - 3z ;::02x + 5y - 5z = 1-x + 5y - 6z = -9

Matrix Review II

Use matrices A, B & C to complete #1-4.

A = l2 OJ-1 2

1) -4A 3) Be 4) BC-2A

Find the value of each determinant for #5 & 6.

2 -15) 14 6

-1 2 46) 6 3 5

-3 7 0

lX+8 -5J l38 -5 J7) Find the values of x & y for which . = is true.3 -y 3 4y-1O

3x+2y =28) Solve using matrix equations.

4x+ y=-4

x+ y+2z=29) Solve using Cramer's Rule: 2x - y + 3z = 5

x-y-z=-2