Difference between revisions of "Manuals/calci/MINVERSE"

Revision as of 05:56, 1 January 2014

MINVERSE(arr)

This function gives the inverse matrix for the given matrix.
We have to find a inverse of a matrix then it should satisfy the following conditions
1.A matrix must be a square matrix.
2.It's determinant not equal to 0.
Let $A<math>bethe2x2matrixwiththeelementsA=|abcd|.*Thentheinverseofmatrix<math>A$ is denoted by $A^{-1}$ .So $A^{-1}={\begin{bmatrix}a&b\\c&d\\\end{bmatrix}}^{-1}={\frac {1}{ad-bc}}*{\begin{bmatrix}d&-b\\-c&a\\\end{bmatrix}}$

</math>

Now let A be the matrix is of order nXn.
Then the inverse of A is A^-1= 1/det(A) . adj(A)
Where adj(A) is the adjoint of A.
Adjoint is the matrix formed by taking the transpose of the co-factor matrix of a given original matrix.
Also A.A^-1=A^-1.A=I, where I is the identity matrix.Non-square matrices do not have inverses.
Not all square matrices have inverses.
A square matrix which has an inverse is called invertible or non-singular, and a square matrix without an inverse is called non-invertible or singular.
This function will return the result as error when

1. Any one of the cell is non-numeric or any cell is empty or contain text
2. Suppose number of rows not equal to number of columns

Matrix A A=(4 3

  3     2)

MINVERSE(B5:C6)=(-2 3

                 3       -4)

MATRIX A A=(3 4

     6       8)

MINVERSE(C4:D5)=Null, because its det value is 0. MATRIX A A=(2 3

  4     7)

MINVERSE(B4:C5)=(3.5 -1.5

               -2           1)

@@ Line 9: / Line 9: @@
 *Let <math>A<math> be the 2x2 matrix with the elements A=|a    b
                                                            c     d|.
-*Then the inverse of matrix <math>A<math> is denoted by A^-1.So A^-1=|a        b|^-=1/ad-bc   |d     -b
+*Then the inverse of matrix <math>A</math> is denoted by <math>A^{-1}</math>.So <math>A^{-1}=\begin{bmatrix}
-                                                                                  -c     a|.
+a & b \\
+c & d \\
+\end{bmatrix}^{-1}= \frac{1}{ad-bc} *   \begin{bmatrix}
+d & -b \\
+-c & a \\
+\end{bmatrix} </math>
+</math>
 *Now let A be the matrix is of order nXn.
 *Then the inverse of A is A^-1= 1/det(A) . adj(A)