Write a matrix equation equivalent to the system of equations.
7x - 8y = -9
-2x - 2y = -2
3
To write a matrix equation equivalent to the system of equations, we can represent the coefficients of the variables and the constant terms in a matrix form.
Let's define a matrix A as the coefficient matrix, a matrix X as the variable matrix, and a matrix B as the constant matrix.
The coefficient matrix A is:
A = [7 -8; -2 -2]
The variable matrix X is:
X = [x; y]
The constant matrix B is:
B = [-9; -2]
The matrix equation equivalent to the given system of equations is:
AX = B
To write a matrix equation equivalent to the given system of equations, we can represent the coefficients of the variables as a matrix, multiply it by the variables' matrix, and set it equal to the matrix of the constants.
Let's represent the variables matrix as X, the coefficients matrix as A, and the constants matrix as B.
The variables matrix X is:
X = | x |
| y |
The coefficients matrix A is:
A = | 7 -8 |
| -2 -2 |
The constants matrix B is:
B = | -9 |
| -2 |
Now, we can write the matrix equation as:
AX = B
After matrix multiplication, it becomes:
| 7 -8 | * | x | = | -9 |
| y | | -2 |
Simplifying this equation, we get:
7x - 8y = -9
-2x - 2y = -2
This matrix equation is equivalent to the given system of equations.
Surely you must have an idea about this one.
What did you get?