Scalar Problems Using Division

 Introduction for scalar problems using division:

The scalar problems usig division represents the operations of the problems in different topics with scalar using division operation The topic represents that the scalar number divides some form. The form may be the matrix in mathematics. The students are basically confusing on the scalar number(it just a number). In this article we are going to discuss about the scalar problems using division operation in matrices for the students in detail. Please express your views of this topic Define Integration by commenting on blog.

Examples for Scalar Problems Using Division

Review on the scalar problem on the division operation originated with the addtiion operation of the two matrices   `P = [[7,7,7],[14,14,14],[14,14,14]]`  and `W = [[154,154,154],[154,154,154],[7,7,7]]`   The operation given by `1/7(P+W)`
Solution:

Here there are two matrices given.

They are in same dimensions.

The elementary positioning is given by

P =   `[[P_11,P_12 ,P_13 ],[P_21 ,P_22 ,P_23 ],[P_31 ,P_32 ,P_33 ]]`    and  W =  `[[W_11,W_12 ,W_13 ],[W_21 ,W_22 ,W_23 ],[W_31 ,W_32 ,W_33 ]]`

`P + W`    is given by  `[[P_11 + W_11,P_12 + W_12,P_13 + W_13],[P_21 + W_21,P_22 + W_22,P_23 + W_23],[P_31 + W_31,P_32 + W_32,P_33 + W_33]]`

P + W =   `[[P_11 + W_11,P_12 + W_12,P_13 + W_13],[P_21 + W_21,P_22 + W_22,P_23 + W_23],[P_31 + W_31,P_32 + W_32,P_33 + W_33]]`

P + W  =  `[[7+154,7+154,7+154],[14+154,14+154,14+154],[14+7,14+7,14+7]]`

P + W  =  `[[161,161,161],[168,168,168],[21,21,21]]`

`1/7(P+W)`  =  `1/7`   `[[161,161,161],[168,168,168],[21,21,21]]`

=     `[[161/7,161/7,161/7],[168/7,168/7,168/7],[21/7,21/7,21/7]]`

=     `[[23,23,23],[24,24,24],[3,3,3]]`  is the result obtained in scalar number division.

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Problems for Scalar Problems Using Division

Review on the scalar problem on the division operation originated with the addtiion operation of the two matrices   `P = [[7,7,7],[14,14,14],[14,14,14]]`  and `W = [[154,154,154],[154,154,154],[7,7,7]]`   The operation given by `1/7P+1/7W`
Solution:

Here there are two matrices given.

They are in same dimensions.

The elementary positioning is given by

`P_1` = `1/7`  P =   ` [[7/7,7/7,7/7],[14/7,14/7,14/7],[14/7,14/7,14/7]]`  =   ` [[1,1,1],[2,2,2],[2,2,2]]`

`W_1` = `1/7`  W =   ` [[154/7,154/7,154/7],[154/7,154/7,154/7],[7/7,7/7,7/7]]` =   ` [[22,22,22],[22,22,22],[1,1,1]]`

`P_1` =    `[[P_11,P_12 ,P_13 ],[P_21 ,P_22 ,P_23 ],[P_31 ,P_32 ,P_33 ]]`    and  `W_1` =  `[[W_11,W_12 ,W_13 ],[W_21 ,W_22 ,W_23 ],[W_31 ,W_32 ,W_33 ]]`

`P_1 + W_1`    is given by  `[[P_11 + W_11,P_12 + W_12,P_13 + W_13],[P_21 + W_21,P_22 + W_22,P_23 + W_23],[P_31 + W_31,P_32 + W_32,P_33 + W_33]]`

`P_1 + W_1`  =   `[[P_11 + W_11,P_12 + W_12,P_13 + W_13],[P_21 + W_21,P_22 + W_22,P_23 + W_23],[P_31 + W_31,P_32 + W_32,P_33 + W_33]]`

`P_1 + W_1`    =  `[[1+22,1+22,1+22],[2+22,2+22,2+22],[2+1,2+1,2+1]]`

`1/7P+1/7W`   `=`       `P_1 + W_1`   =`[[23,23,23],[24,24,24],[3,3,3]]`        is the result obtained in scalar number division.