Identity and inverse matrices
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Identity and Inverse Matrices. 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.

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Identity and Inverse Matrices

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Identity and inverse matrices

Identity and Inverse Matrices


Key topics

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

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 topics1

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

Checking for Inverse Matrices

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


Finding 2x2 inverse matrices

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


Practice

Practice

  • Find the inverse matrix for the following matrices:

N/A


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