Period+8+-+Arithmetic+and+Operations

-Before going into the arithmetic operations of matrices, one must understand the basics of matrices like their size, order, columns and rows, and identity, which are all important aspects to consider when adding, subtracting, scalar multiplying, and transposing matrices. Use this wiki: Properties of Matricesin order to familiarize yourself with matrices before getting into the arithmetic operations of matrices. ( For more information on matrices read Period 6's properties of matrices__)__
 * 2. Matrix Arithmetic and Operations**

-First, in order to add matrices, the matrices must be the same size. When they are the same size, you must add the corresponding entries. These numbers are then listed in a new matrix. For example: -For subtracting, the same rules are applied, the matrices must be the same size and when they are, you must subtract the corresponding entries to create the new matrix. For example: -Clearly, these matrices are the same size, the corresponding entries were added or subtracted, and the final answer is simplified. -After reading and understanding these examples of adding and subtracting matrices, try some of these more difficult examples. -First add the given matrices then subtract them for extra practice.
 * a. Addition and Subtraction**


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-Scalar Multiplication involves multiplying the entire matrix by a number. -To do scalar multiplication, one simply needs to multiply the number or scalar on the outside of the matrix, by each element inside of the matrix. -Think of it as using the distributive property of multiplication; in Algebra if you have 3(x+1), you can distribute the 3 to both the "x" and the "1." This would yield an answer of 3x+3. -When it comes to matrices, just apply the same concept. Distribute the number on the outside, to every single number on the inside. For example: -After reading and understanding scalar multiplication, try these more difficult examples.
 * b. Scalar Multiplication**
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-Transposing a matrix is changing the order of the numbers in the matrix. -Every row of the previous matrix is turned into the column of the new matrix and every column of the previous matrix is turned into the row of the new matrix. For example 1: -This matrix has been transposed where each row is replaced by the column and the other way around.
 * c. Transpose**

-After understanding transposing, try these harder examples.
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-http://www.purplemath.com/modules/mtrxadd.htm -http://www.purplemath.com/modules/mtrxmult.htm -http://programmedlessons.org/VectorLessons/vmch13/vmch13_14.html -http://www.ucl.ac.uk/mathematics/geomath/level2/mat/mat4.html -http://people.hofstra.edu/stefan_waner/realworld/tutorialsf1/frames3_1.html -http://comp.uark.edu/~jjrencis/femur/Learning-Modules/Linear-Algebra/mtxdef/transpose/transpose.html http://hotmath.com/hotmath_help/topics/scalar-multiplication-of-matrices.html http://chortle.ccsu.edu/vectorlessons/vmch13/vmch13_14.html
 * Links:**

By: Blake Ruzich and Anthony Setola