Difference between revisions of "Manuals/calci/MMULT"

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==Examples==
 
==Examples==
−
A student investigated the chance of getting viral fever in a school for a period that took vitamin tablets every day. The total number of students 880. In that 639 students didn't get viral fever and 241 students got fever .But the expected ratio is 1:3<br/>
+
#'''Example 1'''
−
'''Answer'''
+
{| class="wikitable"
−
*If the ratio is 1:3 and the total number of observed individuals is 880, then the expected numerical values should be: 660 will not get fever and 220 students will get fever.  
+
|+Spreadsheet
 +
|-
 +
! !! A !! B !! C !! D!! E
 +
|-
 +
! 1
 +
| 5 || 7 || 8 || ||
 +
|-
 +
! 2
 +
| 7 || 4 ||  ||  ||
 +
|-
 +
! 3
 +
| 8  ||  ||  || ||
 +
|-
 +
! 4
 +
| 4 ||-5  || 9  || ||
 +
|-
 +
! 5
 +
|  ||  ||  || ||
 +
|}
 +
'''From the above table values:'''
 +
{| class="wikitable"
 +
|+ =MMULT(3,A1:A3)
 +
|-
 +
| 15
 +
| 21
 +
| 24
 +
|}
 +
{| class="wikitable"
 +
|+=MMULT(6,A4:C4)
 +
|-
 +
| 24
 +
| -30
 +
| 54
 +
  |}
  
−
{| class="wikitable" style="width:50%"
+
#'''Example 2'''
−
|-
+
{| class="wikitable"
−
!
+
|+Matrix A
−
! No Fever
 
−
! Get Fever
 
 
|-
 
|-
−
! Observed Values
+
| 7 || 5
−
| 639
 
−
| 241
 
 
|-
 
|-
−
! Expected Values
+
| 2 || 3
−
| 660
 
−
| 220
 
 
|-
 
|-
−
! <math>\frac{(oi-ei)^2}{ei}</math>
+
| 6 || 0
−
| 0.668
+
|-
−
| 2
+
| 9 || 8   
 
|}
 
|}
  
−
*The <math>\chi^2</math> value is 2.668
+
{| class="wikitable"
−
*Now <math>df=(r-1)(c-1) = (2-1)(2-1) = 1 </math>
+
|+Matrix B
−
*From the Chi Squared Distribution probability table with <math>df</math> is 1, the <math>\chi^2</math> value of 2.668 is  0.10.<br/>
+
|-
−
CHITEST(or,er) = 0.10
+
| 8 || -4 ||11
 +
|-
 +
| 2 || 7  || 5 
 +
|}
 +
*Here Matrix A is of order 4x2 and Matrix B is of order 2x3.
 +
*So the Product Matrix is of order 4x3. i.e
 +
#'''1st Row''' 7*8+5*2 = 66  ;  7*(-4)+5*7 = 7  ;  7*11+5*5 = 102
 +
#'''2nd Row''' 2*8+3*2 = 22  ;  2*(-4)+3*7 = 13  ;  2*11+3*5 = 37 and so on
  
 
==See Also==
 
==See Also==

Revision as of 07:32, 26 November 2013

MMULT(a1,a2)


  • where and are the array if two matrices

Description

  • This function gives product of two matrices.
  • Matrix multiplication is of two types:
Type 1: A scalar (a constant) is multiplied with the each element of the matrix.
Type 2: Multiplication of two matrices.
  • We can do the matrix multiplication when the number of columns in the first matrix equals the number of rows in the second matrix.
  • For e.g. 4x2 matrix can multiply with 2x3. The matrix product of two arrays and is , where is the row number and is the column number.
  • i.e Multiply the elements of each row of 1st matrix by elements of each column of 2nd matrix.
  • So the resultant matrix is of the order: Rows of 1st matrix × Columns of 2nd.
  • For e.g If we multiply a 4x2 matrix with a 2x3 matrix, the product matrix is of order 4x3 .
  • This function will give the result as error when:
The number of columns in the 1st matrix is not equal to number of rows in the 2nd matrix.
In the range cell, any cells are empty or that should not be convert in to numbers.

Examples

  1. Example 1
Spreadsheet
A B C D E
1 5 7 8
2 7 4
3 8
4 4 -5 9
5

From the above table values:

=MMULT(3,A1:A3)
15 21 24
=MMULT(6,A4:C4)
24 -30 54
  1. Example 2
Matrix A
7 5
2 3
6 0
9 8
Matrix B
8 -4 11
2 7 5
  • Here Matrix A is of order 4x2 and Matrix B is of order 2x3.
  • So the Product Matrix is of order 4x3. i.e
  1. 1st Row 7*8+5*2 = 66 ; 7*(-4)+5*7 = 7 ; 7*11+5*5 = 102
  2. 2nd Row 2*8+3*2 = 22 ; 2*(-4)+3*7 = 13 ; 2*11+3*5 = 37 and so on

See Also

References

CHI-SQUARE Distribution

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