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Stitz-Zeager_College_Algebra_e-book

# As we will see in section 852 determinants specically

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Unformatted text preview: × n matrices, Im A = AIn = A. • Distributive Property of Matrix Multiplication over Matrix Addition: A(B ± C ) = AB ± AC and (A ± B )C = AC ± BC The one property in Theorem 8.5 which begs further investigation is, without doubt, the multiplicative identity. The entries in a matrix where i = j comprise what is called the main diagonal of the matrix. The identity matrix has 1’s along its main diagonal and 0’s everywhere else. A few examples of the matrix Ik mentioned in Theorem 8.5 are given below. The reader is encouraged to see how they match the deﬁnition of the identity matrix presented there. [1] I1 8 10 01 I2 1 100 0 0 1 0 0 001 0 I3 0 1 0 0 0 0 1 0 0 0 0 1 I4 And may not even have the same dimensions. For example, if A is a 2 × 3 matrix and B is a 3 × 2 matrix, then AB is deﬁned and is a 2 × 2 matrix while BA is also deﬁned... but is a 3 × 3 matrix! 484 Systems of Equations and Matrices The identity matrix is an example of what is called a square matrix as it has the same number of rows as...
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