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Identity and Inverse Matrices. The Identity Matrix The identity matrix [I] for multiplication is a square matrix with a 1 for every element of the principal.

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Presentation on theme: "Identity and Inverse Matrices. The Identity Matrix The identity matrix [I] for multiplication is a square matrix with a 1 for every element of the principal."— Presentation transcript:

1 Identity and Inverse Matrices

2 The Identity Matrix The identity matrix [I] for multiplication is a square matrix with a 1 for every element of the principal diagonal (top left to bottom right) and a 0 in all other positions.square matrix element Example: 3x3 Identity Matrix

3 Identity Matrix A = A I = A

4 Inverse Matrix The product of a matrix and its inverse is the identity matrix. A -1 is the notation to designate the inverse of a matrix. A A -1 = I

5 Verify Inverse Matrices: Determine whether the pair of matrices are inverses. Since XY≠ I, they are not inverses!

6 Find the inverse of the matrix. Step 1: Find the determinant. Step 2: Multiply by

7 Find the inverse of the matrix. Step 1: Find the determinant. Step 2: Change the matrix: Step 3: Multiply by.

8 Find the inverse of each matrix. Step 1: Find the determinant of the matrix. Since the determinant equals 0, R -1 does not exist.


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