Suppose $$I_{3}$$ is the3x3 identity matrix and A and B are 3x3 matrices such that:
E _{1}E _{2}A=B
Where:
E _{1} is the elementary matrix obtained by performing
-\frac{ 1 }{ 2 } R _{2} \rightarrow R _{2} on I _{3} , and
E _{2} is the elementary matrix obtained by performing
R _{1} + \frac{ 1 }{ 2 } R _{2} rightarrow R _{1} on I _{3}\]

a) Write down E _{1} and E _{2}
b) Write down E _{1}^{-1} and E _{2}^{-1}
c) Write A as a product of E _{1}^{-1}, E _{2}^{-1}and B

Question

Suppose $$I_{3}$$ is the3x3 identity matrix and A and B are 3x3 matrices such that: 
E _{1}E _{2}A=B
Where:
E _{1} is the elementary matrix obtained by performing 
-\frac{ 1 }{ 2 } R _{2} \rightarrow R _{2} on I _{3}  , and
E _{2} is the elementary matrix obtained by performing 
R _{1} + \frac{ 1 }{ 2 } R _{2} rightarrow R _{1} on  I _{3}\]

a) Write down E _{1} and E _{2}
b) Write down E _{1}^{-1} and E _{2}^{-1}
c) Write A as a product of E _{1}^{-1}, E _{2}^{-1}and B

helder_edwin · Answer

an elementary matrix is the matrix obtained by performing on the identity matrix an elementary operation

amistre64 · Answer

dont forget to use the delimiters to parse the code

`    $$-\frac{ 1 }{ 2 } R _{2} \rightarrow R _{2} on I _{3} $$   `

amistre64 · Answer

$$-\frac{ 1 }{ 2 } R _{2} \rightarrow R _{2} ~on~ I _{3} $$

anonymous · Answer

I have no clue why my question don't want to show in the correct format...

amistre64 · Answer

the part of the program that reads the material in the textarea does not know that you are typing it up in code.  You have to wrap your code in delimiters so that the reader can parse it correctly.