Really simple matrix reduction

In summary, the conversation is about finding the product of four elementary matrices to express matrix A and its inverse A^-1. The process involves performing row operations on the identity matrix and expressing them as a matrix. The product of the matrices at the end of each step should give back the original matrix.
  • #1
NeonVomitt
7
0

Homework Statement



I don't know why I keep getting this wrong...some help would be greatly appreciated.

A =

[ 0 -6 ]
[-2 -3 ]

(1) Write A as a product of 4 elementary matrices:

Wouldn't that just mean to Reduce Row echelon it, and show it in 4 steps?

(2) Write A^-1 as a product of 4 elementary matrices

Wouldn't I just find the inverse of A, and write down the steps?

I did all that and I got it wrong...so maybe if someone could show me, it would really help me out!


Homework Equations




THANKS

The Attempt at a Solution

 
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  • #2
the product of the matrices at the end of each step should give back the original matrix.
 
  • #3
NeonVomitt said:

Homework Statement



I don't know why I keep getting this wrong...some help would be greatly appreciated.

A =

[ 0 -6 ]
[-2 -3 ]

(1) Write A as a product of 4 elementary matrices:

In this case an elementary matrix means a matrix which you obtain by preforming a single row operation on the identity matrix.

Wouldn't that just mean to Reduce Row echelon it, and show it in 4 steps?
Yes but you have to express the row operations as a matrix.

(2) Write A^-1 as a product of 4 elementary matrices

Wouldn't I just find the inverse of A, and write down the steps?
Remember A is expressed as the product of four elementary matrices.

[tex](A_1 A_2 A_3 A_4)^{-1}[/tex]

gives what when the brackets are removed.
 
  • #4
rock.freak667 said:
the product of the matrices at the end of each step should give back the original matrix.

that is what RREF does anyways.

So if,

[ -2 -3 ]
[ 0 -6]

[1 3/2 ]
[0 -6 ]

[ 1 3/2 ]
[ 0 1 ]

[1 0 ]
[0 1 ]

Is that not the answer in four elementary matrix steps for the first question?

And for the second question it is the same, but steps on the other side (inverse matrix)?
 

What is really simple matrix reduction?

Really simple matrix reduction is a mathematical process used to simplify a complex matrix into a simpler form by applying a series of operations such as row operations, column operations, and scalar multiplication.

Why is really simple matrix reduction important?

Really simple matrix reduction is important because it allows us to solve systems of equations, find inverse matrices, and perform other mathematical operations more easily by reducing the complexity of the matrix.

What are the basic steps of really simple matrix reduction?

The basic steps of really simple matrix reduction include identifying the leading entry (the first non-zero element) in each row, using row operations to create zeros below the leading entry, and using column operations to create zeros above the leading entry.

Can really simple matrix reduction be used on any type of matrix?

Yes, really simple matrix reduction can be used on any type of matrix, including square matrices, rectangular matrices, and even matrices with complex numbers.

Are there any limitations to really simple matrix reduction?

While really simple matrix reduction is a useful tool, it is not always possible to reduce a matrix to its simplest form. In some cases, the matrix may be already in its simplest form or may require more complex methods to simplify it.

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