Manuals/calci/MINVERSE

MINVERSE(a)

• $a$ is the array of numeric elements

Description

• 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 $A$ be the 2x2 matrix with the elements

$A={\begin{bmatrix}a&b\\c&d\\\end{bmatrix}}$.

• Then the inverse of matrix $A$ is denoted by $A^{-1}$.

$A^{-1}={\begin{bmatrix}a&b\\c&d\\\end{bmatrix}}^{-1}={\frac {1}{ad-bc}}*{\begin{bmatrix}d&-b\\-c&a\\\end{bmatrix}}$

• Now let $A$ be the matrix is of order $nXn$.
• Then the inverse of $A$ is $A^{-1}={\frac {1}{det(A)}}*adj(A)$
• Where $adj(A)$ is the adjoint of $A$.
• Adjoint is the matrix formed by taking the Transpose of the Co-factor matrix of the 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

ZOS

• The syntax is to calculate the inverse of the matrix in ZOS is $MINVERSE(a)$.
  • $a$ is the array of numeric elements.
• For e.g.,minverse([[10,12],[11,14]])

Examples

$MatrixA={\begin{bmatrix}4&3\\3&2\\\end{bmatrix}}$ $MINVERSE(B5:C6)={\begin{bmatrix}-2&3\\3&-4\\\end{bmatrix}}$

$MatrixA={\begin{bmatrix}3&4\\6&8\\\end{bmatrix}}$ $MINVERSE(C4:D5)=Null$, because its determinant value is 0.

$MatrixA={\begin{bmatrix}2&3\\4&7\\\end{bmatrix}}$ $MINVERSE(B4:C5)={\begin{bmatrix}3.5&-1.5\\-2&1\\\end{bmatrix}}$

See Also

• MMULT
• MDETERM

References

• Matrix Inverse