How can you represent the system of equations with a matrix
11x-12y=7
5x+12y=-7
To represent the given system of equations using a matrix, we need to rewrite the equations in matrix form.
The system of equations is:
11x - 12y = 7
5x + 12y = -7
We can rewrite this system as:
[11 -12 | 7]
[ 5 12 | -7]
This is a matrix representation of the given system of equations. The numbers in the first two columns represent the coefficients of x and y respectively, while the numbers in the last column represent the constant terms on the right side of the equations.
To represent the system of equations with a matrix, you can create a coefficient matrix and a constant matrix.
The coefficient matrix is formed by taking the coefficients of the variables and arranging them in the same order as the variables appear in the equations. In this case, the coefficient matrix is:
| 11 -12 |
| 5 12 |
The constant matrix is formed by taking the constants on the right-hand side of the equations. In this case, the constant matrix is:
| 7 |
|-7 |
Now, you can represent the system of equations as a matrix equation by multiplying the coefficient matrix by a column matrix of the variables and setting it equal to the constant matrix.
| 11 -12 | | x | = | 7 |
| 5 12 | | y | |-7 |
Therefore, the matrix equation representing the system of equations is:
| 11 -12 | | x | = | 7 |
| 5 12 | | y | |-7 |
To represent the system of equations using a matrix, you can create a coefficient matrix and a constant matrix.
The coefficient matrix is constructed by listing the coefficients of the variables (x and y) in the equations. In this case, the coefficient matrix would be:
[11 -12]
[5 12]
The constant matrix is created by listing the constants on the other side of the equal sign. In this case, it would be:
[7]
[-7]
To write the system of equations in matrix form, you combine the coefficient matrix and the constant matrix by placing them side by side:
[11 -12 | 7]
[5 12 | -7]
The vertical line separates the coefficient matrix from the constant matrix.
So, the matrix representation for the given system of equations would be:
[11 -12 | 7]
[5 12 | -7]