Difference between revisions of "Manuals/calci/MINVERSE"

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<div style="font-size:30px">'''MINVERSE(arr)'''</div><br/>
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<div style="font-size:30px">'''MINVERSE(a)'''</div><br/>
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*<math>arr</math> is the  array of numeric elements
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*<math>a</math> is the  array of numeric elements.
 +
**MINVERSE(), returns the matrix inverse of an array.
  
 
==Description==
 
==Description==
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*1.A matrix must be a square matrix.
 
*1.A matrix must be a square matrix.
 
*2.It's determinant not equal to 0.
 
*2.It's determinant not equal to 0.
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*Let <math>A<math> be the 2x2 matrix with the elements A=|a    b
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*Let <math>A</math> be the 2x2 matrix with the elements  
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                                                          c    d|.
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<math>A=\begin{bmatrix}
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*Then the inverse of matrix <math>A</math> is denoted by <math>A^{-1}</math>.So <math>A^{-1}=\begin{bmatrix}
 
 
a & b \\
 
a & b \\
 
c & d \\
 
c & d \\
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\end{bmatrix}^{-1}= \frac{1}{ad-bc} *   \begin{bmatrix}
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\end{bmatrix}</math>.
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*Then the inverse of matrix <math>A</math> is denoted by <math>A^{-1}</math>.
 +
:<math>A^{-1}=\begin{bmatrix}
 +
a & b \\
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c & d \\
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\end{bmatrix}^{-1}= \frac{1}{ad-bc} * \begin{bmatrix}
 
d & -b \\
 
d & -b \\
 
-c & a \\
 
-c & a \\
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\end{bmatrix} </math>
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\end{bmatrix}
 
</math>
 
</math>
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*Now let A be the matrix is of order nXn.
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*Now let <math>A</math> be the matrix is of order <math>nXn</math>.
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*Then the inverse of A is A^-1= 1/det(A) . adj(A)
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*Then the inverse of <math>A</math> is <math>A^{-1}= \frac{1}{det(A)}*adj(A)</math>
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*Where adj(A) is the adjoint of A.
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*Where <math>adj(A)</math> is the adjoint of <math>A</math>.
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*Adjoint is the matrix formed by taking the transpose of the co-factor matrix of a given original matrix.
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*Adjoint is the matrix formed by taking the Transpose of the Co-factor matrix of the original matrix.
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*Also A.A^-1=A^-1.A=I, where I is the identity matrix.Non-square matrices do not have inverses.
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*Also <math>A.A^{-1}=A^{-1}.A = I</math>, where <math>I</math> is the identity matrix.
 +
*Non-square matrices do not have inverses.
 
*Not all square matrices 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.
 
*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.
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  2. Suppose number of rows not equal to number of columns
 
  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 <math>MINVERSE(a)</math>.
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**<math>a</math> is the  array of numeric elements.
 +
*For e.g.,minverse([[10,12],[11,14]])
  
 
== Examples ==
 
== Examples ==
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Matrix A
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<math>Matrix A=
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A=(4     3
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\begin{bmatrix}
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  3     2)
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4 & 3 \\
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MINVERSE(B5:C6)=(-2       3
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3 & 2 \\
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                  3       -4)
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\end{bmatrix}
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MATRIX A
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</math>
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A=(3       4
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<math>
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      6       8)
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MINVERSE(B5:C6)=
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MINVERSE(C4:D5)=Null, because its det value is 0.
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\begin{bmatrix}
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MATRIX A
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-2 & 3 \\
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A=(2     3
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3 & -4 \\
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  4     7)
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\end{bmatrix}
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MINVERSE(B4:C5)=(3.5     -1.5
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</math>
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                -2           1)
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 +
<math>Matrix A=
 +
\begin{bmatrix}
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3 & 4 \\
 +
6 & 8 \\
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\end{bmatrix}
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</math>
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<math>MINVERSE(C4:D5)=Null</math>, because its determinant value is 0.
 +
 
 +
<math>Matrix A=
 +
\begin{bmatrix}
 +
2 & 3 \\
 +
4 & 7 \\
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\end{bmatrix}
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</math>
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<math>MINVERSE(B4:C5)=  
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\begin{bmatrix}
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3.5 & -1.5 \\
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-2 & 1 \\
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\end{bmatrix}
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</math>
 +
 
 +
 
 +
==Related Videos==
  
 +
{{#ev:youtube|01c12NaUQDw|280|center|Inverse of Matrix}}
  
 
==See Also==
 
==See Also==
  
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*[[Manuals/calci/COS | COS]]
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*[[Manuals/calci/MMULT | MMULT ]]
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*[[Manuals/calci/TAN | TAN]]
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*[[Manuals/calci/MDETERM | MDETERM ]]
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*[[Manuals/calci/ASIN| ASIN]]
 
−
*[[Manuals/calci/DSIN | DSIN]]
 
  
 
==References==
 
==References==
  
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*[http://en.wikipedia.org/wiki/Trigonometric_functions List of Trigonometric Functions]
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*[http://en.wikipedia.org/wiki/Invertible_matrix Matrix Inverse]
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*[http://en.wikipedia.org/wiki/Sine SIN]
+
 
 +
 
 +
 
 +
 
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 16:02, 24 July 2018

MINVERSE(a)


  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is the array of numeric elements.
    • MINVERSE(), returns the matrix inverse of an array.

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} be the 2x2 matrix with the elements

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=\begin{bmatrix} a & b \\ c & d \\ \end{bmatrix}} .

  • Then the inverse of matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} is denoted by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A^{-1}} .
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} be the matrix is of order Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle nXn} .
  • Then the inverse of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A^{-1}= \frac{1}{det(A)}*adj(A)}
  • Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle adj(A)} is the adjoint of .
  • Adjoint is the matrix formed by taking the Transpose of the Co-factor matrix of the original matrix.
  • Also Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A.A^{-1}=A^{-1}.A = I} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle MINVERSE(a)} .
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is the array of numeric elements.
  • For e.g.,minverse([[10,12],[11,14]])

Examples

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Matrix A= \begin{bmatrix} 4 & 3 \\ 3 & 2 \\ \end{bmatrix} } Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle MINVERSE(B5:C6)= \begin{bmatrix} -2 & 3 \\ 3 & -4 \\ \end{bmatrix} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Matrix A= \begin{bmatrix} 3 & 4 \\ 6 & 8 \\ \end{bmatrix} } Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle MINVERSE(C4:D5)=Null} , because its determinant value is 0.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Matrix A= \begin{bmatrix} 2 & 3 \\ 4 & 7 \\ \end{bmatrix} } Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle MINVERSE(B4:C5)= \begin{bmatrix} 3.5 & -1.5 \\ -2 & 1 \\ \end{bmatrix} }


Related Videos

Inverse of Matrix

See Also

References



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