Question

Решить систему линейных уравнений с помощью матрицы обратной 4Х+У-2Z=10 -X+3Y-Z=-1 3X-Y+5Z=1 это всё в одной скобке

Answer 1

X=2 
y=0
z=-1 
Вот правильно сам проходил такое.

Answer 2

Solving the System of Linear Equations using Matrix Inversion

To solve the system of linear equations using matrix inversion, we can represent the system in matrix form and then use the inverse of the coefficient matrix to find the solution. The given system of linear equations is:

**4X - 2Y - Z = 10 -X + 3Y - Z = -1 3X - Y + 5Z = 1**

We can represent this system in matrix form as:

|  4  -2  -1  |   | X |   |  10  |
| -1   3  -1  |   | Y | = |  -1  |
|  3  -1   5  |   | Z |   |   1  |

Using Matrix Inversion to Solve the System

To solve for X, Y, and Z, we can use the formula:

X = A^-1 * B

Where A is the coefficient matrix and B is the constant matrix.

The inverse of matrix A, denoted as A^-1, can be calculated using the formula:

A^-1 = 1/det(A) * adj(A)

Where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A.

Calculating the Inverse of the Coefficient Matrix

The first step is to calculate the determinant of matrix A:

det(A) = 4(3*5 - (-1)(-1)) - (-2)(-1*5 - (-1)(3)) - (-1)(-1*3 - 3*(-2))

After calculating the determinant, we can then find the adjugate of matrix A.

Finding the Solution

Once we have the inverse of matrix A, we can use it to find the solution for X, Y, and Z using the formula:

X = A^-1 * B

By substituting the values of A^-1 and B into the formula, we can find the values of X, Y, and Z.

This process will provide the solution to the given system of linear equations.