1. Solving Linear Systems Syed Nasrullah
Lab 3
Solving Linear Systems
Syed Nasrullah

2. Method 1 Finding Determinants To Solving Linear Systems 2 × 2 matrix

3. Example : - Compute the determinants of the following matrices :
det(A) = (1)(4) - (2)(3) = = -2. - +
det(A) = (3)(5)(5) + (1)(9)(2) + (4)(1)(6) - (3)(9)(6) - (1)(1)(5) - (4)(5)(2) =
= -90

4. Finding Determinants using Matlab

5. Solving Linear Systems “ using Determinates ”
Determinants can be used to find out if a linear system of equations has a solution. Consider the following set of equations: 5x + 2y − 9z = 44 −9x − 3y + 2z = 11 6x + 7y + 3z =5
1’st step :
find the determinant of the coefficient matrix A.

6. The solution of the system
2’nd step :
create a column vector of the numbers on the right-hand side of the system. Then using left division, and the vector which will appear is the solution of the linear equation.
Left Division
= b / A
The solution of the system

7. Method 2 Finding the Inverse of a Matrix To Solving Linear Systems
The Identity Matrix ( I ) is the n × n matrix , each main diagonal entry is a 1 and for which all other entries are 0. For Example

11. [ -ͨ ᵃ ] Solve the linear equation “ using inverse Matrix ” :
B= 5 2
A =1/(ad-bc) [ ᵈ -ᵇ ]
[ -ͨ ᵃ ]
A = 1 /[ (3*(-2)-(-2) *(6) ]
X = A * B =
3x − 2y = 5
6x − 2y = 2 -1 -1 -1

12. Solving Linear Systems “ using inverse Matrix ”
5x + 2y − 9z = 44 −9x − 2y + 2z = 11 6x + 7y + 3z = 44
Solving Linear Systems “ using inverse Matrix ”
1’st step :
find the inverse of the coefficient matrix A.

13. The solution of the system
2’nd step :
create a column vector (B) of the numbers on the right-hand side of the system.
Then using Multiplication * between inverseA and B which will appear is the solution of the linear equation.
The solution of the system

14. Find a solution to the following Linear Equations:
EXCERSIZE :
Find a solution to the following Linear Equations:
x + 2y + 3z = 12
−4x + y + 2z = 13
9y − 8z = −1