Solution of system of linear equations using inverse of Matrix Method

Описание: This video explains how to solve a system of linear equations using the inverse of a matrix method (0:05). This method is applicable only if the coefficient matrix is invertible, meaning its determinant is not equal to zero (1:12).

Here's a breakdown of the process:
• Formulating the equation (1:34): The system of linear equations is represented as Ax = b, where 'A' is the coefficient matrix, 'x' is the variable vector, and 'b' is the constant vector.
• Checking invertibility (3:10): Calculate the determinant of matrix 'A'. If it's not zero, the matrix is invertible, and the method can be applied. The example in the video shows a determinant of 19, confirming invertibility (3:41).
• Calculating the inverse matrix (3:55): To find 'x', you need to calculate A-inverse (A⁻¹). This can be done using the formula A⁻¹ = (Adjoint of A) / (Determinant of A) (4:08). The video briefly mentions finding the adjoint by calculating cofactors and then transposing the cofactor matrix (4:24).
• Solving for variables (4:58): Once A⁻¹ is found, multiply it by the constant vector 'b' (x = A⁻¹b) to get the values of the variables (x, y, z) (5:02). The video demonstrates this calculation, resulting in x = 6/19, y = 10/19, and z = 4/19 (5:41).

The video concludes by stating that this method provides a way to solve linear equations using matrix inverses and hints at a more general method for solving linear equations in the next video (6:02).


Solving system of linear equations using inverse of matrix method
System of linear equations
Solving system of linear equations (non-homogeneous and homogeneous)
Solving system of linear equations using matrices
Solving system of linear equations using inverse of coefficient matrix intermediate



Adjoint | Cofactor | Inverse of Matrix using Adjoint
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