Mathematics 1229A/B Lecture 15: Lecture 15

• School: Western University
• Department: Mathematics
• Course: Mathematics 1229A/B
• Professor: Mohsen Mollahajiaghaei

Document Summary

Ii 231 f 1 4: i 2 8 y wesometimesreferto an mxlmatrixas acolumnrectorand a ixn matrixa rowvector. Amatrixis a squareif ithasthesamenumberofrowsascolumns inthissituationthenumberof rows or columnsiscalledtheorderofthematrix. Capitalletters areusedtodenotematricesandtheentriesof amatrixaredenotedbythe correspondinglowercaseletterwith doublesubscripts as an example wecandescribe a 3 3matrix as. A yaa i as as as3 a entryrow i column j. 7 o 3: o 2 biz 2 b22 0 bz 0. Let aandbbematriceswiththesamedimensions thesum of a and bwitten at b isthe matrixobtainedbyaddingcorrespondingentries of aandb. I at t it lt: 22il undefined nt. it. Multiplicationby a scalar let a be a matrixand c be ascalar thenthescalarmultipleca isthematrixobtained by multiplyingeachentry of aby c. Azeromatrix denotedby 0 is a matrixofanydimensionsconsisting ofonlyzeroentries h. Matrixmultiplication let aand bbematrices suchthatthenumber ofcolumns of a isequaltothenumber of rows of b leta beonxn and bbenxg thentheproductofab is themxamatrix csuchthattheentry intheithrowandjthcolumnofc is thedotproduct of therow of aandthejhcolumnof b. Example find ab and ba where a i.