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Identity and Inverse matrices

Identity and Inverse matrices. Section 4.4. Identity matrix. For matrices, the n X n identity matrix is the matrix that has 1’s on the main diagonal and 0’s elsewhere. Properties of an identity matrix. If A is any n X n matrix and I is the n X n identity matrix then

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Identity and Inverse matrices

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  1. Identity and Inverse matrices Section 4.4

  2. Identity matrix For matrices, the n X n identity matrix is the matrix that has 1’s on the main diagonal and 0’s elsewhere.

  3. Properties of an identity matrix If A is any n X n matrix and I is the n X n identity matrix then IA = A and AI = A

  4. Inverse matrices Two n X n matrices are inverses of each other if their product (in both orders) is the n X n identity matrix AB = I and BA = I or

  5. The inverse of a 2 X 2 matrix a b If A = c d then A inverse = d -b 1/det A -c a

  6. Solving a matrix equation To solve the matrix equation AX = B for X, multiply both sides on the left by the inverse of matrix A

  7. Solving a matrix equation (continued)

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