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Arty
Arty, Computer Software Engineer
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I want a pseudo code for the following 1) A pseudo to write

Resolved Question:

I want a pseudo code for the following:

1) A pseudo to write a program that can solve simultaneous equation of two variables
2) Pseudo to write a program that will add 2 matrices together
3) Pseudo code to write a program to subtract two matrices
4) pseudo code to write a program that can solve a quadratic equation.

Please, Its on Qbasic that I want to write the program, so the pseudo code should be one that i can use on Qbasic.
Submitted: 6 years ago.
Category: Programming
Expert:  Arty replied 6 years ago.

 

1) Suppose the following is our linear equation:

A11*X+A12*U=B1

A21*X+A22*Y=B2

 

A11, A12, A21, A22, B1 and B2 are numeric constants

X and Y are unknown (to be found)

 

pseudocode:

 

INPUT A11, A12, B1

INPUT A21, A22, B2

LET D = (A11 * A22 - A12 * A21)

IF D = 0 THEN

PRINT this equation has no unique solution

ELSE

LET X = (B1 * A22 - B2 * A12) / D

LET Y = (B2 * A11 - B1 * A21) / D

PRINT X, Y

END IF

 

2) Pseudo to write a program that will add 2 matrices together

 

A(N, M) and B(N, M) - matrices to add,

C(N, M) - resulting matrix

 

pseudocode:

INPUT N

INPUT M

REM DEFINE MATRIXES

DIM A(N, M)

DIM B(N, M)

DIM C(N, M)

REM READ A MATRIX

FOR ROW = 1 TO N

FOR COL = 1 TO M

INPUT A(ROW, COL)

NEXT COL

NEXT ROW

REM READ B MATRIX

FOR ROW = 1 TO N

FOR COL = 1 TO M

INPUT B(ROW, COL)

NEXT COL

NEXT ROW

REM PERFORM ADDITION

FOR ROW = 1 TO N

FOR COL = 1 TO M

LET C(ROW, COL) = A(ROW, COL) + B(ROW, COL)

NEXT COL

NEXT ROW

REM OUTPUT RESULT

FOR ROW = 1 TO N

FOR COL = 1 TO M

PRINT C(ROW, COL)

NEXT COL

NEXT ROW

 

3) Pseudo code to write a program to subtract two matrices

REM READING CODE FOR A, B, N and M is the same as in 2)

REM SUBTRACT CODE FOLLOWS

FOR ROW = 1 TO N

FOR COL = 1 TO M

LET C(ROW, COL) = A(ROW, COL) - B(ROW, COL)

NEXT COL

NEXT ROW

REM OUTPUT CODE IS THE SAME AS IN 2)

 

4) pseudo code to write a program that can solve a quadratic equation.

let the following quatratic equation

A*X^2 + B*X + C = 0

where A, B, C are constants and X is unknown value

here is a pseudocode

 

INPUT A, B, C

LET D = B * B - 4 * A * C

IF D < 0 THEN

PRINT Equation has no solutions

ELSE IF D = 0 THEN

LET X = -B/(2*A)

PRINT Equation has only one solution

PRINT X

ELSE

LET X1 = (-B + SQRT(D))/(2*A)

LET X2 = (-B - SQRT(D))/(2*A)

PRINT Equation has two solutions

PRINT X1, X2

END IF

 

 

Hope this helps.

 

Regards,

Arty



Edited by Arty on 6/17/2010 at 6:50 AM EST
Customer: replied 6 years ago.

Please I also want the Algorithms and the problem analysis for each problem.

Thank you very much for your understanding

Expert:  Arty replied 6 years ago.

Ok.

 

Algorithms can be expressed with pseudo-code. But they can also be written in simple words. Here is an analysis and algorithm.

 

1) Analysis.

To solve a linar equation, like this:

graphic

where a11, a12, a21, a22, b1, b2 - some fixed numbers and x1, x2 are unknowns,

one should use this formula:

to find X1:

graphic

 

to find X2:

graphic

 

The divisor can't be zero:

graphic

 

So we should check the divisor first, then try to find values.

 

The algorithm is:

- ask user to input known coefficients: a11, a12, a21, a22, b1, b2

- calculate D, that is a11*a22 - a12*a21

- if D is zero - the equation can't be solved

- if D is non zero - calculate x1 and x2 according to the above formula

 

2) Analysis.

 

Only matrices of the same dimentions can be added. Let N is a number of rows, M is a number of columns. Sum of matrices A and B is a matrix C, that has the same dimentions NxM and in the position of any row i and column j there is a sum of corresponding elements (i,j) of matrices A and B.

 

so the algorithm is:

 

- create matrix C with the same dimentions as A and B

- for every row and column of matrix C set element to be equal the sum of appropriate elements of A and B, i.e. C(row, column) = A(row, column) + B(row, column)

 

3) Subtraction of matrices is basically the same as addition. C(row, column) = A(row, column) - B(row, column).

 

4) Quadratic equation looks like:

a*X^2 + b*X +c = 0

 

a, b and c are numbers, X is unknown variable

 

there is a known formula to calculate unknown X:

X = (-b +/- SquareRoot(b^2 - 4*a*c))/(2*a)

 

This equation may have 1, 2 or 0 solutions depending on this expression value: (b^2 - 4*a*c). If it is equal to 0, there is only one solution:

X=(-b)/2*a

If it is below zero - there are no solutions

If it is above zero - there are 2 solutions

X= (-b + SquareRoot(b^2 - 4*a*c))/(2*a)

and

X= (-b - SquareRoot(b^2 - 4*a*c))/(2*a)

 

Algorithm.

- ask user to enter a, b and c

- calculate d = (b^2 - 4*a*c)

- if d<0 print a message that there are no solutions

- if d=0 print a message that there is only 1 solution, X=-B/(2*a)

- if d>0 print a message that there are 2 solutions: X=(-B+square_root(D))/(2*a) and X=(-B-square_root(D))/(2*a)

- exit

 

Regards

Arty

Customer: replied 6 years ago.
Please one final thing before I finally accept the answer. I need the actual code too. Thanks
Expert:  Arty replied 6 years ago.

Hi.

 

Here are all 4 files.

 

Regards,

Arty

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