find a solution to the following set of equations x + 2y + 3z = 12 −4x + y + 2z = 13 9y − 8z = −1 what is the determinant of the coeffi cient matrix? in matlab

In MATLAB, we can use the built-in function det to find the determinant of a matrix. To solve the system of equations, we first need to represent them in matrix form. Let's call the coefficient matrix A and the solution vector b. Then we have:

main.m
| 1  2  3 |   | x |     | 12 |
| -4 1  2 | * | y |  =  | 13 |
| 0  9 -8 |   | z |     | -1 |
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We can write this as Ax = b. To find x, we can use the formula x = A^-1 * b. However, before we can take the inverse of A, we need to make sure that det(A) is not zero. If det(A) = 0, then the matrix A is singular and the system of equations has no unique solution.

To find det(A), we can use the following code in MATLAB:

main.m
A = [1 2 3; -4 1 2; 0 9 -8];
detA = det(A);
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The output will be detA = -247.

Since det(A) is not zero, we can find the solution x using the following code:

main.m
b = [12; 13; -1];
x = A \ b;
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The backslash operator \ solves the system of equations by finding the solution x that satisfies Ax = b. The output will be x = [1; 2; -1], which is the unique solution to the system of equations.