Difference between revisions of "Manuals/calci/MINVERSE"
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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''MINVERSE'''(Array) where, '''Array''' - represents array having equal number of rows and columns. </di...") |
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− | <div | + | <div style="font-size:30px">'''MINVERSE(arr)'''</div><br/> |
+ | *<math>arr</math> 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 <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 | ||
+ | -c a|. | ||
+ | *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 | ||
− | |||
− | + | == Examples == | |
+ | 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) | ||
− | |||
− | |||
− | |||
− | + | ==See Also== | |
− | + | *[[Manuals/calci/COS | COS]] | |
− | + | *[[Manuals/calci/TAN | TAN]] | |
− | + | *[[Manuals/calci/ASIN| ASIN]] | |
+ | *[[Manuals/calci/DSIN | DSIN]] | ||
− | + | ==References== | |
− | + | *[http://en.wikipedia.org/wiki/Trigonometric_functions List of Trigonometric Functions] | |
− | + | *[http://en.wikipedia.org/wiki/Sine SIN] | |
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Revision as of 04:44, 1 January 2014
MINVERSE(arr)
- 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 <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
-c a|.
- 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
Examples
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)