Solve the set of linear equations by the matrix method:a+3b+2c=3,2a-b-3c=-8,5a+2b+c=9 sove for a
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To solve the set of linear equations using the matrix method, we need to represent the system of equations as a matrix equation in the form AX = B, where A is the coefficient matrix, X is the solution vector, and B is the constant vector.
Given the system of equations:
a + 3b + 2c = 3 ---> Equation 1
2a - b - 3c = -8 ---> Equation 2
5a + 2b + c = 9 ---> Equation 3
Step 1: Create the coefficient matrix A
The coefficient matrix A is obtained by taking the coefficients of the variables from each equation and arranging them row-wise:
A = [[1, 3, 2],
[2, -1, -3],
[5, 2, 1]]
Step 2: Create the constant vector B
The constant vector B is obtained by taking the constants from the right-hand side of each equation and arranging them as a column vector:
B = [[3],
[-8],
[9]]
Step 3: Solve for X
To solve for X, we need to find the inverse of matrix A and then multiply it by vector B:
X = A^(-1) * B
Let's calculate:
Step 4: Calculate the inverse of A
Find the inverse of matrix A.
Step 5: Multiply A^(-1) by B
Multiply the inverse of A by the constant vector B.
Once you have performed these calculations, you will obtain the solution vector X, which will consist of the values of a, b, and c.