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Identity and Inverse MatricesPowerPoint Presentation

Identity and Inverse Matrices

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Presentation Transcript

Key Topics

- Identity matrix: a square matrix, multiplied with another matrix doesn’t change the other matrix (just like 1 is the multiplicative identity of real numbers)

Identity Matrix in Action

Notice: These two matrices are the same. Multiplying by the identity matrix changed nothing

Notice: These two matrices are the same. Multiplying by the identity matrix changed nothing

Key Topics

- You might be wondering: why do I tell you about the identity matrix ?? If it doesn’t do anything, why do we need to know what it is ??
- Inverses: two nXn matrices are inverses of each other if their product is the identity matrix

Checking for Inverse Matrices

- Determine whether the following pairs of matrices are inverses of one another:

Finding 2X2 Inverse Matrices

- To find the inverse of a 2X2 matrix, use the following method:

Rearranged matrix

Inverse of Determinant

If determinant is 0 there is no inverse!!

Basically this tells us to calculate the determinant, then multiply it’s inverse by the rearranged matrix having a and d switch places and b and c as the opposite values

A-1 is the notation used to represent the inverse of matrix A

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