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Matrices, Matrix Addition is 3. Distributive under scalar Multiplication k(A+B) = kA + kB, Matrices can be treated as Individual objects for Mathematical Operations, Matrix Addition for example <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfenced open="[" close="]"> <mtext> 1 15 -3 4 </mtext> </mfenced> <mtext> + </mtext> <mfenced open="[" close="]"> <mtext> 2 -9 -1 5 </mtext> </mfenced> <mtext> = </mtext> <mfenced open="[" close="]"> <mtext> 3 6 -4 9 </mtext> </mfenced> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfenced open="[" close="]"> <mtext> 1 0 0 0 1 0 0 0 1 </mtext> </mfenced> </mrow> </math> is also a diagonal matrix;Notice that in a square matrix of n columns and n rows there will be a diagonal of n elements. In this example, those are the only non-zero elements of the matrix, Matrices are related to Vectors, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfenced open="[" close="]"> <mtext> 2 3 5 6 7 8 </mtext> </mfenced> <mtext> </mtext> </mrow> </math> is a 2x3 matrix; It has 2 rows and 3 columns, Matrix Multiplication for example, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfenced open="[" close="]"> <mtext> 2 -1 3 0 6 4 </mtext> </mfenced> <mtext> * </mtext> <mfenced open="[" close="]"> <mtext> 1 2 4 3 -2 6 </mtext> </mfenced> <mtext> = </mtext> <mfenced open="[" close="]"> <mtext> -8 19 16 42 </mtext> </mfenced> </mrow> </math>, Scalar Multiplication for example, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> 2 </mtext> <mfenced open="[" close="]"> <mtext> 1 0 -3 4 2 7 </mtext> </mfenced> <mtext> = </mtext> <mfenced open="[" close="]"> <mtext> 2 0 -6 8 4 14 </mtext> </mfenced> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfenced open="[" close="]"> <mtext> 1 0 0 0 1 0 0 0 1 </mtext> </mfenced> </mrow> </math> is a 3x3 matrix; It has 3 rows and 3 columns, Inverse Matrix can be denoted <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mmultiscripts> <mtext> M </mtext> <none/> <mtext> -1 </mtext> </mmultiscripts> <mtext> (the inverse of matrix M) </mtext> </mrow> </math>
