Introduction on elementary column operations:
According to the term elementary Column operation are found to be one of the parts in matrix. Elementary is found be defined as Elementary matrix is found to be defined as a simple matrix where it represented in different identity matrix form. Elementary column operation is the operation that is done by post or right multiplication. I like to share this Complex Fractions with you all through my article.
Rules Based on Elementary Column Operations:
Rule 1: To find the sum given, of elementary column operator, the identity matrix operation is applied.
Rule 2: The post multiplication has to be done for carry out elementary column operations.
Rule 3: The column operator is created from multiplying “column * column"
Representation of Column in Matrix:
The column is represented in matrix as : `[[a],[b],[c]]`
Example Problems Based on Elementary Column Operations:
Example 1:
Elementary column operation on the term “A”, where the identity used in matrix `A= [[1,6], [4,1], [0,1]]` and identy matrix `x = [[1,0], [0 ,1]]`
Solution:
Given: Identity matrix `x = [[1,0], [0 ,1]]`
`A= [[1,6], [4,1], [0,1]]`
Step 1: The given identity matrix x is interchanged of fist and second column and the finding result is named it (x1).
Step 2: To do the elementary column operation on given `A= [[1,6], [4,1], [0,1]]`
Step 3: The operation in matrix is done by [row *column]
`X= [[1,0], [0,1]]`
The first and second column is interchanged and the result is,
`X1= [[0,1], [1,0]].`
Now, the found X1 is calculated with given “A”
`A= [[1,6], [4,1], [0,1]]`
`X1= [[0,1], [1,0]]`
`A*X1` for calculation elementary column operation on
`A*X1`
` [[1,6], [4,1], [0,1]] * [[0,1], [1,0]]`
` [[1*0+6*1 , 1*1+6*0],[4*0+1*1 , 4*1+1*0],[0*0+1*1, 0*1+1*0]]`
`[[0+6, 1+0], [0+1,4+1], [0+1, 0+0]]`
`[[6,1],[1,4],[1,0]]`
Hence ,the elmentary column operation for the given value `A=[[6,1],[1,4],[1,0]]`
Example 2:Based on elementary column operations
Elementary column operation on the term “D”, where `D= [[1,2],[1,1],[0,0]] ` the identity used in matrix `"x= [[1,0],[0,1]] `
Solution:
Given: Identity matrix `x = [[1,0], [0 ,1]]`
`"D= [[1,2], [1,1],[0,0]], `
Step 1: The given identity matrix x is interchanged of fist and second column and the finding result is named it (x1).
Step 2: To do the elementary column operation on given `D=[[1,2],[1,1],[0,0]]`
Step 3: The operation in matrix is done by [row *column]
`X= [[1,0], [0,1]]`
The first and second column is interchanged and the result is,
`"X1= [[0,1],[1,0]]`
Now, the found X1 is calculated with given “A”
`D= [[1,2], [1,1], [0,0]]`
`X1= [[0,1], [1,0]]`
`D*X1` for calculation elementary column operation on
`D*X1`
`[[1,2], [1,1], [0,0]]*[[0,1], [1,0]]`
`[[1*0+2*1 , 1*1+2*0],[1*0+1*1 , 1*1+1*0],[0*0+0*1, 0*1+0*0]]`
`[[0+2, 1+0], [0+1,1+0], [0+0, 0+0]]`
`[[2,1],[1,1],[0,0]]`
Hence ,the elementary column operation for the given value `D=[[2,1],[1,1],[0,0]]`
Understanding free help with math word problems is always challenging for me but thanks to all math help websites to help me out.
Problems to be Solved Based Elementary Column Operations:
Elementary column operation on the term “S”, where `S ` = `[[6,2],[2,1],[9,4]]` the identity used in matrix `X` = `[[1,0],[0,1]] `
Answer: The elementary column operation of `S` =`[[2,6],[1,2],[4,9]]`
Elementary column operation on the term “Z”, where `Z` =`[[2,1],[3,2],[6,3]]` the identity used in matrix `X` = `[[1,0],[0,1]] `
Answer: The elementary column operation of `Z` =`[[1,2],[2,3],[3,6]]`
According to the term elementary Column operation are found to be one of the parts in matrix. Elementary is found be defined as Elementary matrix is found to be defined as a simple matrix where it represented in different identity matrix form. Elementary column operation is the operation that is done by post or right multiplication. I like to share this Complex Fractions with you all through my article.
Rules Based on Elementary Column Operations:
Rule 1: To find the sum given, of elementary column operator, the identity matrix operation is applied.
Rule 2: The post multiplication has to be done for carry out elementary column operations.
Rule 3: The column operator is created from multiplying “column * column"
Representation of Column in Matrix:
The column is represented in matrix as : `[[a],[b],[c]]`
Example Problems Based on Elementary Column Operations:
Example 1:
Elementary column operation on the term “A”, where the identity used in matrix `A= [[1,6], [4,1], [0,1]]` and identy matrix `x = [[1,0], [0 ,1]]`
Solution:
Given: Identity matrix `x = [[1,0], [0 ,1]]`
`A= [[1,6], [4,1], [0,1]]`
Step 1: The given identity matrix x is interchanged of fist and second column and the finding result is named it (x1).
Step 2: To do the elementary column operation on given `A= [[1,6], [4,1], [0,1]]`
Step 3: The operation in matrix is done by [row *column]
`X= [[1,0], [0,1]]`
The first and second column is interchanged and the result is,
`X1= [[0,1], [1,0]].`
Now, the found X1 is calculated with given “A”
`A= [[1,6], [4,1], [0,1]]`
`X1= [[0,1], [1,0]]`
`A*X1` for calculation elementary column operation on
`A*X1`
` [[1,6], [4,1], [0,1]] * [[0,1], [1,0]]`
` [[1*0+6*1 , 1*1+6*0],[4*0+1*1 , 4*1+1*0],[0*0+1*1, 0*1+1*0]]`
`[[0+6, 1+0], [0+1,4+1], [0+1, 0+0]]`
`[[6,1],[1,4],[1,0]]`
Hence ,the elmentary column operation for the given value `A=[[6,1],[1,4],[1,0]]`
Example 2:Based on elementary column operations
Elementary column operation on the term “D”, where `D= [[1,2],[1,1],[0,0]] ` the identity used in matrix `"x= [[1,0],[0,1]] `
Solution:
Given: Identity matrix `x = [[1,0], [0 ,1]]`
`"D= [[1,2], [1,1],[0,0]], `
Step 1: The given identity matrix x is interchanged of fist and second column and the finding result is named it (x1).
Step 2: To do the elementary column operation on given `D=[[1,2],[1,1],[0,0]]`
Step 3: The operation in matrix is done by [row *column]
`X= [[1,0], [0,1]]`
The first and second column is interchanged and the result is,
`"X1= [[0,1],[1,0]]`
Now, the found X1 is calculated with given “A”
`D= [[1,2], [1,1], [0,0]]`
`X1= [[0,1], [1,0]]`
`D*X1` for calculation elementary column operation on
`D*X1`
`[[1,2], [1,1], [0,0]]*[[0,1], [1,0]]`
`[[1*0+2*1 , 1*1+2*0],[1*0+1*1 , 1*1+1*0],[0*0+0*1, 0*1+0*0]]`
`[[0+2, 1+0], [0+1,1+0], [0+0, 0+0]]`
`[[2,1],[1,1],[0,0]]`
Hence ,the elementary column operation for the given value `D=[[2,1],[1,1],[0,0]]`
Understanding free help with math word problems is always challenging for me but thanks to all math help websites to help me out.
Problems to be Solved Based Elementary Column Operations:
Elementary column operation on the term “S”, where `S ` = `[[6,2],[2,1],[9,4]]` the identity used in matrix `X` = `[[1,0],[0,1]] `
Answer: The elementary column operation of `S` =`[[2,6],[1,2],[4,9]]`
Elementary column operation on the term “Z”, where `Z` =`[[2,1],[3,2],[6,3]]` the identity used in matrix `X` = `[[1,0],[0,1]] `
Answer: The elementary column operation of `Z` =`[[1,2],[2,3],[3,6]]`
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