1. solve this system using matrices:
3.7x-2.3+4.2z=8
2.6+4.6y-3.9z=10
8x+2z=20
2. Write this system as a matrix equation:
-2x+y=8
7x-3y=10
To solve the system using matrices, we need to represent the given equations in matrix form.
1. Solve the system using matrices:
The given system of equations is:
3.7x - 2.3 + 4.2z = 8 -- (Equation 1)
2.6 + 4.6y - 3.9z = 10 -- (Equation 2)
8x + 2z = 20 -- (Equation 3)
To represent the system in matrix form, we can create a coefficient matrix, a variable matrix, and a constant matrix.
The coefficient matrix (A) consists of the coefficients of the variables x, y, and z:
A = [3.7 0 4.2;
0 4.6 -3.9;
8 0 2]
The variable matrix (X) consists of the variables x, y, and z:
X = [x; y; z]
The constant matrix (B) consists of the constant terms on the right-hand side of the equations:
B = [8; 10; 20]
The system can now be represented as a matrix equation:
AX = B
Now, to solve for X, we need to find the inverse of matrix A, denoted as A^(-1), and multiply it with matrix B:
X = A^(-1)B
By finding the inverse of matrix A and performing the matrix multiplication, we can obtain the values of x, y, and z.
2. Write this system as a matrix equation:
The given system of equations is:
-2x + y = 8 -- (Equation 1)
7x - 3y = 10 -- (Equation 2)
To represent this system as a matrix equation, we can create a coefficient matrix, a variable matrix, and a constant matrix.
The coefficient matrix (A) consists of the coefficients of the variables x and y:
A = [-2 1;
7 -3]
The variable matrix (X) consists of the variables x and y:
X = [x; y]
The constant matrix (B) consists of the constant terms on the right-hand side of the equations:
B = [8; 10]
The system can now be represented as a matrix equation:
AX = B
To solve for X, we need to find the inverse of matrix A, denoted as A^(-1), and multiply it with matrix B:
X = A^(-1)B
By finding the inverse of matrix A and performing the matrix multiplication, we can obtain the values of x and y.
#2
the square matrix
-2 1
7 -3
multiplied by the column matrix
x
y
=
8
10
(I can't think of another way to print matrices on this board)
1. I can't make out your equations.