Write a matrix to represent the following system.
{ -5 + 3y = 4
{ 2x - 9y = 7
I have six boxes to fill in.
(-5 3)(x) = (4)
(2 -9)(y) = (7)
the extra = sign is just to improve spacing
To represent the system of equations using a matrix, we can write the coefficient matrix and the constant matrix.
The coefficient matrix contains the coefficients of the variables:
| -5 3 |
| 2 -9 |
The constant matrix contains the constants on the right-hand side of the equations:
| 4 |
| 7 |
Therefore, the matrix representation of the system is:
| -5 3 |
| 2 -9 |
| 4 |
| 7 |
To represent the given system of equations in matrix form, we can write the coefficients of the variables and the constants in a matrix.
Let's assign x to the first variable and y to the second variable.
The matrix representation of the system is:
[2 -9] [x] = [7]
[-5 3] [y] [4]
Here's how we fill in the six boxes:
- The top left box represents the coefficient of x, which is 2.
- The top right box represents the coefficient of y, which is -9.
- The bottom left box represents the coefficient of x in the second equation, which is -5.
- The bottom right box represents the coefficient of y in the second equation, which is 3.
- The boxes in the first column represent the constants on the right side of the equations. The box at the top represents the constant in the first equation, which is 7. The box at the bottom represents the constant in the second equation, which is 4.
By organizing the coefficients and constants in this matrix form, we can solve the system of equations using various methods, such as matrix operations, elimination, or substitution.