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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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