MATHS :: Lecture 21 :: Solving simulteneous equation and cramers rule
INVERSE OF A MATRIX
Let A be any square matrix. If there exists another square matrix B Such that AB = BA = I (I is a unit matrix) then B is called the inverse of the matrix A and is denoted by A-1.
The cofactor method is used to find the inverse of a matrix. Using matrices, the solutions of simultaneous equations are found.
Introduction to Vectors
Vector Dot Product and Vector Length
Matrix Vector Products
Matrices to solve a vector combination problem
Converting a line from Cartesian to vector form
Working Rule to find the inverse of the matrix
Step 1: Find the determinant of the matrix.
Step 2: If the value of the determinant is non zero proceed to find the inverse of the matrix.
Step 3: Find the cofactor of each element and form the cofactor matrix.
Step 4: The transpose of the cofactor matrix is the adjoint matrix.
Step 5: The inverse of the matrix A-1 =
Find the inverse of the matrix
Let A =
The value of the determinant is non zero
Let Aij denote the cofactor of aij in
The matrix formed by cofactors of element of determinant is
\adj A =
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