Chapter 5 - linear systems study guide - MA129 Week 5 Linear Systems of Equations and Matrices 1 Matrices A matrix is a rectangular array of numbers

# Chapter 5 - linear systems study guide - MA129 Week 5...

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MA129 Week 5 - Linear Systems of Equations and Matrices 1.MatricesA matrix is a rectangular “array” of numbers where the numbers individually are called entries.IfAm×nis amatrix, then it hasmrows,ncolumns, andm×nentries.Example:A=24-1630is a 3×2 matrix with 3 rows, 2 columns, and 6 entries.Matrix Operations:SupposeAandBare twom×nmatrices (i.e. the same size!) andcis constant. Then:(i)A+Bis found by adding the entries ofAto the corresponding entries inB.(ii)A-Bis found by subtracting the entries ofBfrom the corresponding entries inA.(iii)cAis found by multiplying every entry inAbyc.(iv)ABis undefined as multiplication may only occur when the number of columns ofAequalsthe number of rows ofB.Note:If the number of columns inAequals the number of rows inB,thenABcan be determined.ABwill then have the same number of rows asAand the same number of columns asB.Each entryabijin the resulting matrix is obtained by multiplying corresponding entries inrow
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