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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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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