## Question

## Transcribed Text

1- - For linear equations of
find the solution for x and y, using:
a. Row picture (geometrical method; manually)
b. Column picture (geometrical method; manually)
C. Matrix form (numerical method; manually)
2- Solve the previous problem for
038
Either of manual computation or software programing are acceptable in this problem.
3- Write a MATLAB program that receives matrix A and regardless of its dimension, would
return its inverse as output, by using elimination method.
4- Use elimination method to find the inverse matrix of
1
2
1
4 3 4 3
A=54321
42224
01201
After manual calculation, use your MATLAB code in previous problem to check your
answer.
5- A linear system with matrix equation of AX=b = (in R3) could be considered as three planes
with/without intersections. Find all configurations (of planes) which do not result in a unique
solution for this equation.
6- Compute L (total elimination matrix) and U (upper-triangular matrix resulted from
eliminating A) for the symmetric matrix A:
aaaa
abbb
A =
abcc
=LU
abcd
find four conditions on a, b, c, d SO that the elimination could be applied on A. After manual
calculation, use MATLAB in order to verify your results.

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Q4 MATLAB

A=[1 2 1 2 1;3 4 3 4 3;5 4 3 2 1;4 2 2 2 4;0 1 2 0 1];

>> [C,D,S,Inverse] = prob(A)

C(:,:,1) =

1 0 0 0 0

-3 1 0 0 0

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

C(:,:,2) =

1 0 0 0 0

0 1 0 0 0

-5 0 1 0 0

0 0 0 1 0

0 0 0 0 1

C(:,:,3) =

1 0 0 0 0

0 1 0 0 0

0 0 1 0 0

-4 0 0 1 0

0 0 0 0 1

C(:,:,4) =

1 0 0 0 0

0 1 0 0 0

0 0 1 0 0...

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