Matrix math is a very complex subject but it has a broad range of important appl
ID: 2912640 • Letter: M
Question
Matrix math is a very complex subject but it has a broad range of important applications. One application you have seen is with respect to solving a system of linear equations. They are also a very beneficial in modeling fields such as cryptology, representing multidimensional objects in physics,
Explain how you see the relationship between the three elementary row operations performed on an augmented matrix and the operations that lead to equivalent systems of equations. What advantages do you see in converting a system of equations to an equivalent augmented matrix? Research a particular application of matrices explaining how a matrix is used. Based on what you have selected think about the three operations of addition, scalar multiplication, and matrix multiplication. Can you describe what the results actually mean? Note that in some applications some of these operations may not have meaning. If that is the case, explain why.
Explanation / Answer
To explain this let me consider a system of linear equations with 3 variables as follows
2x+3y+4z=20
x+5y+z=18
4x+6y+7z=56
This can be modeled as matrix form AX=B
When we do any row operations it means that we are not changing the actual matrix but we are copying the new values to another matrix.
In order to solve this we will try to get the augumented matrix [A | B]. Wee will perform row operations on this augumented matrix to get reduced echelon form. This form makes the last row with one variable and last but one with two variables and left first row with 3 variables. This helps in solving the equations easily.