8.3 The Inverse Of a square Matrix
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10 Terms
Good Video on finding inverse of 2×2
Good video Inverse Matrices Solving Systems of Equations
Key
Formula Super important =This
important thing = This
Example=This
Super important one of =THIS
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Definition of a unique solution
3 variables and 3 equations one solution for each
Properties of Inverses
sin(sin-1x)=x
sin-1x(sinx)=x
f(f-1x))=x
f-1x(f(x)=x
Identity function f(x)=x
Identity Matrix Definition and How it is used in Inverses
The identity Matrix is the Reduced- Row Echelon Form of a Coefficient Matrix. for 3×3 it is [1 0 0, 0 1 0, 0 0 1]
It is a square matrix (nxn)
How it is used in inverses
For inverses it is used as the check to see if it is the inverse
acting as the multiplicative identity (). It acts like the number "1" in scalar multiplication. Inverses are defined by , where multiplying a matrix by its inverse yields the identity matr
![<ul><li><p>The identity Matrix is the <strong>Reduced- Row Echelon Form of a Coefficient Matrix</strong>. for 3×3 it is [1 0 0, 0 1 0, 0 0 1]</p></li><li><p>It is a square matrix (nxn)</p></li></ul><p></p><p><strong><em><u><mark data-color="#fdff4d" style="background-color: rgb(253, 255, 77); color: inherit;">How it is used in inverses </mark></u></em></strong></p><p>For inverses it is used as the check to see if it is the inverse </p><p></p><p><span>acting as the multiplicative identity (). It acts like the number "1" in scalar multiplication. Inverses are defined by , where </span><strong><mark data-color="rgba(0, 0, 0, 0)" style="background-color: rgba(0, 0, 0, 0); color: inherit;">multiplying a matrix by its inverse yields the identity matr</mark></strong></p>](https://assets.knowt.com/user-attachments/27d8f018-0035-4716-b1be-a552d27bc99f.png)
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