How can you represent the system of equations with a matrix?
2x+y=9
x-6y=-1
Kindly help me go about solving this. Thank you so much
AX = B
where A is the matrix of coefficients
X is the column matrix with rows x,y
B is the column matrix with rows 9,-1
See
https://www.wolframalpha.com/input/?i=%7B%7B2%2C1%7D%2C%7B1%2C-6%7D%7D*%7B%7Bx%7D%2C%7By%7D%7D%3D%7B%7B9%7D%2C%7B-1%7D%7D
To represent a system of equations with a matrix, you can use the coefficients of the variables in the equations. In this case, your system of equations is:
2x + y = 9 (Equation 1)
x - 6y = -1 (Equation 2)
To represent this system with a matrix, you can create a coefficient matrix by taking the coefficients of the variables and arranging them in rows. Then, you can create a constant matrix by taking the constant terms on the other side of the equation and arranging them in a column. Finally, you can combine these matrices to form an augmented matrix.
The coefficient matrix for this system is created by taking the coefficients of x and y:
| 2 1 |
| 1 -6 |
The constant matrix is created by taking the constant terms on the other side of the equations:
| 9 |
|-1 |
Then, you can combine these matrices to form the augmented matrix:
| 2 1 | 9 |
| 1 -6 | -1 |
Now, to solve the system of equations using this matrix, you can use various methods such as Gaussian elimination, matrix inversion, or using the inverse of the coefficient matrix.
I can go ahead and solve this system of equations using Gaussian elimination. Would you like me to proceed with that?