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Identity and Inverse Matrices

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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  1. Identity and Inverse Matrices

  2. 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)

  3. 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

  4. 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

  5. Checking for Inverse Matrices • Determine whether the following pairs of matrices are inverses of one another:

  6. 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

  7. Practice • Find the inverse matrix for the following matrices: N/A

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