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3 unknowns, 1 matrix, and 1 variable ...

Asked by: The function 95
linear-algebra
Yesterday at 12:29 PM
1  4

Dear everyone,

Ive been looking at this problem ive got, but i cant find out what would make it work. I can put numbers in a matrix, i can solve 3 unknowns with 3 equations. But now there is a variable, and the variable causes the solution to give either: 1 solution, no solution, or more than one solution. 

I can "brush the matrix" as they say it in Dutch, but im learning Maple so it can go a lot faster than manual labor. So is there a way to do it with Maple? 

Figure 4.1 gives from left to right: 1 solution, no solution, and an indefinite amount of solutions.

Questions: For what value of p, a. gives 1 solution? b. gives no solution? c. gives more than 1 solution?

Now i got Maple to tell me how much p x1, x2, and x3 was, but its not bringing me anywhere to where i can get to a solution. 

A manual method is given in this example. Manual is way way to slow for what i need to achieve, ive got some large big books with mechanics, dynamics, statics, fluid mechanics, concrete calcutions, chemistry etc. waiting for me. I can never achieve that manually in the same time as i could do it with maple. :S 

> 

#example of how to do a solve of a matrix with 3 variables:
> 

stelsel := {x1+x2+x3 = 4, 3*x1+x2-5*x3 = -10, 3*x1+2*x2-x3 = 1}

{x1+x2+x3 = 4, 3*x1+x2-5*x3 = -10, 3*x1+2*x2-x3 = 1}

 (1)
> 

solve(stelsel, {x1, x2, x3})

{x1 = -7+3*x3, x2 = 11-4*x3, x3 = x3}

 (2)
> 

#now the example number 15
> 

stelsel := {(2-p)*x2+x3 = 2, -x1+2*x2+(2-p)*x3 = 0, (1-p)*x1+2*x2+2*x3 = p+3}

{(2-p)*x2+x3 = 2, -x1+2*x2+(2-p)*x3 = 0, (1-p)*x1+2*x2+2*x3 = p+3}

 (3)
> 

solve(stelsel, {x1, x2, x3})

{x1 = -(p^2-6)/(p^2-4*p+4), x2 = -(2*p-5)/(p^2-4*p+4), x3 = 1/(-2+p)}

 (4)
> 

``

Thank you!

Greetings,

The Function

Download Mapleprimes_Question_Book_2_Paragraph_4.2_Example_15.mw

I need help writing the maple code application?...

Asked by: delvin 15
homework pde dsolve
September 11 2022
0  2

Hi
Can someone help me write the program for this equation?
I really need this program.
With respect

 

recursive formula...

Asked by: Carlos Barrera 5
sum summation
September 07 2022
1  5

I hava a recursive formula with variable n. The answer has the variable n and also N1.  What doe N1 mean?

How to collect the coeffects from the equation ...

Asked by: Sradharam 100
coefficients
September 04 2022
0  6

How_to_collect_Coefficent.mw

Kindly help me to find the coefficients from the equation. I have attached the MAPLE file here.

Thank You 

It may seem like a stupid question. ...

Asked by: The function 95
complex 2dmath
August 31 2022
1  3

It may seem like a stupid question, but why is the first answer not complete, but the second imput is the same as what the book states?

I know you dont need to be able to read Dutch to understand that A = amplitude (amplitude), Omega = Hoekfrequentie (Angular frequency), and Varphi= Fasehoek (phase angle). 

They state that fc(0)= A*e^i*varpi, but it clearly shows that the equation on the left of the equal sign gives a "2" and on the right it gives "2+ 2*i*sqrt3".

Why is this so? It does not make things more easy if you can make "mistakes" like that by just asking the answer, but maple spits out half an answer... 

He thanks a lot guys!

Greetings,

The Function 

p.s.
I scanned my math books, i like it, i can search in the book now with the "ctrl+f" function in Adobe reader. Get a scanner. Mine is a Canon Lide 400. Not regretting it.. :) 
Download Mapleprimes_Book_2_Question_3.6.mw
 

> 

omega := 5

5

 (1)
> 

`ϕ` := (1/3)*Pi

(1/3)*Pi

 (2)
> 

A := 4

4

 (3)
> 

"f(t):=A*cos(omega*t+`ϕ`)""+A*I*sin(omega*t+`ϕ`)"
 

proc (t) options operator, arrow, function_assign; A*cos(omega*t+varphi) end proc

  

(4*I)*sin((1/3)*Pi+5*t)

 (4)
> 

f(0)

2

 (5)
> 

A*exp(I*`ϕ`)

2+(2*I)*3^(1/2)

 (6)
> 

NULL

``

Download Mapleprimes_Book_2_Question_3.6.mw

global optima package...

Asked by: MANUTTM 10
package optimization global
August 30 2022
0  2

What is the procedure to add global optima package in maple?

How do I solve this equation?...

Asked by: FDS 105
vector duplicate-question
August 25 2022
0  8

Dear power users, could someone be so kind to help me out with this file and give me some explanation on what I did wrong?

QuestionMaplePrimes.mw Thank you for you time and help

Why does the precedure not solve?...

Asked by: FDS 105
procedure
August 23 2022
0  9

I am still learning Maple and so I would like to rely on you power users to help me out. I probably doing something which is not allowed or not using the best method. I would appreciate any advice. Thank you in advance    ProcQuestion.mw 

Is it possible to fit data with units?...

Asked by: FDS 105
units fit
August 08 2022
0  4

Fitting procedures in Maple are self explaning and easy to perform. However, I was wondering if it is possible to fit data vectors with units. For example one vector would have units of seconds and the other units of length. Thank you for your help.

Maple code for finding optimum maximum value of fu...

Asked by: MANUTTM 10
optimization syntax homework
August 06 2022
2  15

Maple code for finding optimum maximum value of function TOTP given below when D is kept in the range of 300 to 2000?Also give maple code to find 3Dplot to determine the convexity of function TOTP with respect to y and Sr?

make consistent 3D plot out of point values...

Asked by: yasi 30
plotting incomplete-question edited-question
July 26 2022
1  16

I want the resulting shape of the 3D matrix M (ٍExcel file) to be placed in below grids codes.
The range of x and y is between 0 and 1 and the range of z is 1/1 e-4 to 1/1 e-10.

PlotTest.xlsx


 

``

> 

grids := proc (M, x_min, x_max, y_min, y_max) local z_min, z_max, plot_f, xz, yz, xy; z_min := 0.11e-6; z_max := 0.1e-2; plot_f := plot3d(M, x = x_min .. x_max, y = y_min .. y_max); xz := plot3d([x, y_min, z], x = x_min .. x_max, z = z_min .. z_max, style = line, color = blue, thickness = 0, grid = [6, 6]); yz := plot3d([x_min, y, z], y = y_min .. y_max, z = z_min .. z_max, style = line, color = blue, thickness = 0, grid = [6, 6]); xy := plot3d([x, y, z_min], x = x_min .. x_max, y = y_min .. y_max, style = line, color = blue, thickness = 0, grid = [6, 6]); return plots:-display(plot_f, xz, yz, xy, lightmodel = none, tickmarks = [6, 6, 6], labels = [x, y, "Error"], labeldirections = [horizontal, horizontal, vertical], axes = frame, orientation = [45, 70, 0], view = 0.11e-6 .. 0.1e-2) end proc
> 

grids(M, 0, 1, 0, 1)

Warning, expecting only range variables [x, y] in expression M to be plotted but found name M

  

 
> 

``
> 

``


 

Download eeeeeee.mw

Is it possible to stack to dataframe columns?...

Asked by: FDS 105
vector dataframe
June 30 2022
1  3

Perhaps a silly question but is it possible to stack two dataframe columns? When I use the Vector command the columns are stacked but nested.

Thank you for your help

Newton Raphson method for grade 12...

Asked by: AHSAN 115
step-by-step rootfinding numeric
June 12 2022
1  3

Could any one please guide me how to show this solution by using Newton Raphson method. I need to show this solution step by step as shown in example.

Need to view solution step by step...

Asked by: AHSAN 115
solve step-by-step factor
June 12 2022
0  5

Hi Community, I have solved the some basic expression by using built in command to get solution. Now i am interested to view the solution stp by step to show  my students of grade 10.

> 

restart
> 

t := x^6+2*x^5-3*x+2+(2*x^6-4*x+8)

3*x^6+2*x^5-7*x+10

 (1)
> 

p := 2*x^2-x-10

2*x^2-x-10

 (2)
> 

factor(p)

(x+2)*(2*x-5)

 (3)
> 

s := 2*x^2-x-10

2*x^2-x-10

 (4)
> 

solve(s = 0, {x})

{x = 5/2}, {x = -2}

 (5)
> 

sqrt(x-4) = 4

(x-4)^(1/2) = 4

 (6)
> 

solve(sqrt(x-4) = 4, {x})

{x = 20}

 (7)
> 

s := (x^2-9)/(x^2-2*x-15)

(x^2-9)/(x^2-2*x-15)

 (8)
> 

simplify(%)

(x-3)/(x-5)

 (9)
> 

(3*x^2-5*x)*(4*x^2+7*x+4)

(3*x^2-5*x)*(4*x^2+7*x+4)

 (10)
> 

expand(%)

12*x^4+x^3-23*x^2-20*x

 (11)
> 

``

Solving a system of equations:

> 

x+2*y = 4

x+2*y = 4

 (12)
> 

3*x+4*y = 6

3*x+4*y = 6

 (13)
> 

solve({x+2*y = 4, 3*x+4*y = 6}, {x, y})

{x = -2, y = 3}

 (14)
> 

abs(3*x+3) = 12

3*abs(x+1) = 12

 (15)
> 

``
> 

solve(abs(3*x+3) = 12, {x})

{x = 3}, {x = -5}

 (16)
> 

``

Download Help_to_view_solution_step_by_step.mw

Is it possible to filter a dataframe based upon a ...

Asked by: FDS 105
dataframe string filter
May 30 2022
1  2

I know you can filter a dataframe by putting constraints on the numeric columns. However, I would like to sort and filter based upon a given string in a column, is this possible? I cannot immediately find this in the help files. Thank you for your assistance.QuestionDataFrame.mw

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