Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 7.2, Problem 8CP
Extrapolate the approximate solutions in Computer Problem 6. Use the formula
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3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following.
a. Give a geometric description of nullspace(A). Justify.
b. Is A invertible? Justify.
c. Give a geometric description of the span of the column vectors of A. What
space are the column vectors of A in? Justify.
d. What is determinant of A? Justify.
2. Consider the matrix:
A
||
1
1
-3
14
2 1 01
4 1
2
2
-26
1 -3
1 5]
a) What is rank(A)?
b) Is A invertible? Justify.
c) Find the nullspace(A). Justify.
d) Is the trivial solution the only solution to Ax=0? Justify.
e) What is the span of the column vectors of A? Justify.
E
5. Suppose that S={v € R²: v = [2x² - 3]}. Is S a subspace of R²? Prove or disprove
Chapter 7 Solutions
Numerical Analysis
Ch. 7.1 - Use Theorem 7.1 to prove that the boundary value...Ch. 7.1 - Show that the solutions to the BVPs in Exercise 1...Ch. 7.1 - Consider the BVP { y=cyy(a)=yay(b)=yb where c0, ab...Ch. 7.1 - Consider the BVP { y=cyy(0)=0y(b)=0 where c0. For...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Show that the solutions to the linear BVPs {...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Apply the Shooting Method to the linear BVPs....
Ch. 7.1 - Carry out the steps of Computer Problem 1 for the...Ch. 7.1 - Apply the Shooting Method to the nonlinear BVPs....Ch. 7.1 - Carry out the steps of Computer Problem 3 for the...Ch. 7.1 - Prob. 5CPCh. 7.1 - Verify that (7.10) is a solution of the BVP for...Ch. 7.1 - Set compressibility to the moderate value c=0.01 ....Ch. 7.1 - Prob. 3SACh. 7.1 - Change pressure to p=3.5, and resolve the BVP....Ch. 7.1 - Prob. 5SACh. 7.1 - Carry out Step 5 for the reduced compressibility...Ch. 7.1 - Carry out Step 5 for increased compressibility...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to plot solutions to the...Ch. 7.2 - (a) Find the solution of the BVP y=y, y(0)=0,...Ch. 7.2 - Solve the nonlinear BVP 4y=ty4, y(1)=2, y(2)=1 by...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Prob. 9CPCh. 7.2 - Use finite differences to solve the equation {...Ch. 7.2 - Solve { y=cy(1y)y(0)=0y(1/2)=1/4y(1)=1 for c0,...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Carry out the steps of Computer Problem 1, using...Ch. 7.3 - Carry out the steps of Computer Problem 2, using...
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- 6. Suppose that V1, V2 ER", show that span{v1, v2} is a subspace of Rn.arrow_forwardRa X 2) slots per pole per phase 3/31 180 Ko Sin (1) Kdl 1 sin (4) sin(3) Sin (30) اذا مرید شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 Fo lasa! G s.1000-950 20:05 1000 Capper losses: 5kw Rotor input lookw 0.05 ined sove in peaper I need a detailed solution on paper please 6) 1 ۳/۱ وه اذا ميريد شرح الكتب فقط look DC 7) rotov Find the general solution of the following equations: +4y=tan2x 3 7357 Find the general solution of the following equations: - Qll y + y (³) = 0. 101arrow_forwardNC Current Students - North Ce X | NC Canvas Login Links - North ( X Final Exam Comprehensive x Cengage Learning x WASTAT - Final Exam - STAT → C webassign.net/web/Student/Assignment-Responses/submit?dep=36055360&tags=autosave#question3659890_9 Part (b) Draw a scatter plot of the ordered pairs. N Life Expectancy Life Expectancy 80 70 600 50 40 30 20 10 Year of 1950 1970 1990 2010 Birth O Life Expectancy Part (c) 800 70 60 50 40 30 20 10 1950 1970 1990 W ALT 林 $ # 4 R J7 Year of 2010 Birth F6 4+ 80 70 60 50 40 30 20 10 Year of 1950 1970 1990 2010 Birth Life Expectancy Ox 800 70 60 50 40 30 20 10 Year of 1950 1970 1990 2010 Birth hp P.B. KA & 7 80 % 5 H A B F10 711 N M K 744 PRT SC ALT CTRLarrow_forward
- B: 18060 msl Kd Ka, Sin (n) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW /0001 Rotor input 5 : loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط ١٥٠ 7) rotov DC ined sove in Deaper I need a detailed solution on paper please dy x+2y-4 = dx 2x-y-3 Find the general solution of the following equations: 02//yl-4y+13y=esinarrow_forward1) R₂ = X2 2) slots per pole per phase = 3/31 B msl kd 180 60 Kal Sin (1) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW Rotor input: 5 0.05 loo kw 6) 1 /0001 اذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please Q1// Find the solution of: 'y' = x² +376 x4+316 xyo Q2 Find the solution of the initial-valued problems: ex-y y' +exarrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw ined sove in peaper I need a detailed solution on paper please Q3// x²y// +xy/ + (x² - ½) y = x³/². اذا ميريد شرح الكتب فقط look 7) rotor DC Q4// x²y// - (2x+x²)y/ + (2 + x)y = x³. dy 2x+2y+4 = dx 2x-y-3arrow_forward
- ۳/۱ R2X2 2) slots per pole per phase = 3/31 B, 18060 msl Kas Sin() 1sin() sin(30) Sin (30) kd اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speeds S = 1000-950 1000 Copper bosses 5kw 120*50 loca G Rotor input 5 loo kw 6) 1 0.05 اذا ميريد شرح الكتب فقط lookw 7) rotor DC ined sove in peaper I need a detailed solution on paper please 064 Q1// Find the solution of QI/Find the solution of Inxy= 7357 x+2y³ y' = xy3arrow_forwardR₂ = X2 2) slots per pole per phase 3/31 msl 180 60 Kd Ka Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120*50 1000 6 S = 1000-950 1000 Copper bosses: 5kw Rotor input 5 0.05 : loo kw 6) 1 اذا ميريد شرح الكتب فقط 100 7) rotor DC ined sove in peaper I need a detailed solution on paper please Find the general solution of the following equations: Q2lyl-4y+13y=esinx. Find the general solution of the following equations: " Qly (49) - 16y= 0. 151arrow_forward۳/۱ R₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw اذا میرید شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper dy please 04 12=-cosx.y + 2cosx with y(x) = 1 か 'Oy + xlny + xe")dx + (xsiny + xlnx +*dy=0. 01arrow_forward
- ٣/١ R2X2 2) slots per pole per phase = 3/31 B, 18060 msl kd Kas Sin (1) 1sin() sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speeds S = 1000-950 1000 Copper bosses 5kw 120*50 loca G Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط lookw 7) rotor ined sove in peaper I need a detailed solution on paper please DC 口 04 on its wheels as shown in figure. The the door is 8 m below the free surface o is located at the center of the d no water leaks an accident and lands at the bottom of the lake 12m high and I m wide, and the top edge of water Determine the hydrostatic force on the discuss if the driver can open the door, if ong person can lift 100 kg, the passenger The door can be approximated as a vertical rec | 279|-|(23+2+12+20=2) AA Find the general solution of the following equations: 11 - 1/4+xy/-(1-x²³)= 0. 2arrow_forward۳/۱ : +0 العنوان I need a detailed drawing with explanation R₂ = X2 2) slots per pole per phase 3/31 Le msl 180 60 Kd Ka Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120*50 1000 6 S = 1000-950 1000 Copper bosses: 5kw Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط ١٥٠ 7) rotov DC ined sove in peaper I need a detailed solution on paper please 064 Q1// Find the solution of: ( texty Q1// Find the solution of: '' y' -2y= 22% √y³arrow_forwardR2X2 2) slots per pole per phase = 3/31 B-180-60 msl kd Ka, Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses 5kw 120 50 G Rotor input 5 loo kw 6) 1 ۳/۱ 0.05 إذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please Find the general solution of the following equations: " yll + 4y = tan2x. Find the general solution of the following equations: 01-24+7=0 T el [A] G ха =T Marrow_forward
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