Final answer:
To write the system as a vector equation, we list the coefficients of each variable as components of a vector in the equation. To write the system as a matrix equation, we can use the coefficients of the variables to form a matrix and the variables as a column vector.
Step-by-step explanation:
To write the system as a vector equation, we list the coefficients of each variable as components of a vector in the equation. For the given system:
4x1 - x2 = 6
2x1 + 10x2 = 2
6x1 - x2 = 1
We can rewrite it as:
[4, -1] · [x1, x2] = 6
[2, 10] · [x1, x2] = 2
[6, -1] · [x1, x2] = 1
To write the system as a matrix equation, we can use the coefficients of the variables to form a matrix and the variables as a column vector. For the given system:
4x1 - x2 = 6
2x1 + 10x2 = 2
6x1 - x2 = 1
We can rewrite it as:
[4, -1; 2, 10; 6, -1] · [x1; x2] = [6; 2; 1]
Compete Question:
write the system first as a vector equation and then as a matrix equation.
4x1 - x2 = 6
2x1 + 10x2 = 2
6x1 - x2 = 1