COMPUTING FOR ENGINEERS
COMPUTING FOR ENGINEERS ENGR 1371
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This 17 page Class Notes was uploaded by Wilhelm Bechtelar on Saturday October 3, 2015. The Class Notes belongs to ENGR 1371 at Armstrong Atlantic State University taught by Priya Goeser in Fall. Since its upload, it has received 32 views. For similar materials see /class/217869/engr-1371-armstrong-atlantic-state-university in Engineering and Tech at Armstrong Atlantic State University.
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Date Created: 10/03/15
Computing for Engineers ENGRI 3 71 Chapter 12 Matrices Dr Priya Thamburaj Goeser A Review on Matrices o A matrix is an array of numbers represented as shown where n is the number of rows in the matrix and m is the number of columns Column 3 112 113 lm a21 122 023 12m ROW2 A an anZ 1113 anm Arrays amp Matrices Store data in same form Difference is in the de nition of certain Operations size of a matrix The size of a matrix is given by n x m if nm the matrix is known as a square matrix Column 3 all 6112 113 alm 6121 122 123 a2 ROW 2 A an a112 an3 anm Matrix Addition or Subtraction MATLAB command AB all an bll biz A 6 21 6 22 a B b21 b22 a31 a32 3X2 b31 32 3X2 a11b11 alZ b12 AB a21b21 a22b22 a31 b31 6 32 b32 3X2 For addition and subtraction size of A 2 size of B Multiplication of a matrix by a scalar MATLAB command 10A all 6112 A 6 21 6 22 6 31 6 32 3X2 10a11 10a12 10gtltA10a21 10a22 10a31 10a32 3X 2 Scalar multiplication an 8 12 a1n b11 b12 6 21 822 a2n b21 b22 mxn Bmxn am1 am2 39 39 39 amn bm1 bm2 a11Xb11 a12Xb12 a1nXb1n a21 x b21 a22 x b22 32 x b2n gt am1 X bm1 am2 x bm2 39 39 amn X bmn Matrix Multiplication An X m Bm XI Cn xl g4 Interior dimensions are equal multiplication is possible Exterior dimensions define the dimensions of the result Matrix Multiplication MATLAB command AB a1 1 a12 A an an Bb11 biz 913 914 921 b22 b23 b24 2X4 a32 3x2 allbll a12b21 allblz a12b22 61111913 61121923 a11b14 a12b24 A X B a21b11 a22b21 a21b12 a22b22 a21b13 a22b23 a21b14 a22 b24 a31b11 a32b21 a31b12 a32b22 a31b13 a32b23 a31b14 a32b24 3X 4 Matrix multiplication an a12 b11 b12 b13 Amxn 821 a22 Bmxn b21 b22 b23 am1 am2 311 X b11 a12X b21 a11X b12 393112 X b22 an X b13 a12X b23 gt 821 X b11 a22X b21 321 X b12 a22X b22 a21X b13 8122 X baa 331 X b11 a32 X b21 a31X b12 a32 X b22 331 X b13 332 X baa Inverse of a matrix 0 MATLAB command inVA A all alZ A IAZIZI 0 a21 an O 1 a22 a12 6122 6112 A1 2 a21 all a11a22 a12a21 allazz a12a21 IAI 6 21 all allazz a12a21 a11a22 a12a21 16111 16112 16121 16122 gtA1 Transpose of a matrix MATLAB command transposeA or A39 all 6112 A 6 21 6 2 a31 a32 3X2 ATa11 6 21 6 31 an 6 22 6 32 2X3 Linear Algebraic Equations Linear algebraic equations are of the general form a11x1 aux2 alnxn 2 b1 6121361 anx2 612an 2 b2 an1x1 anzx2 amxn 2 bn Where the a s are constant coef cients and b s are constants and n is the number of equations Linear Algebraic Equations Matrix form a11x1 aux2 alnxn 2 b1 6121361 anx2 aann 2 b2 an1x1 anzx2 amxn 2 bn AX B a1 1 a21 aln x1 b1 a21 a22 a2n x2 b2 anl anZ arm xn bn Example Use Gauss elimination to solve the following system of equations 30x1 01x2 02x3 785 01x1 70x2 03x3 193 03x1 02x2 le3 2 714 Priya Thamburaj Goeser Exampie Ciear Define the system of equations A30 01 02 01 70 03 03 02 100 b785 193 714 Soive for x in Axb usin Gauss Eiimination g XAb Verification bverifyAx X 30000 25000 70000 bverify 78500 193000 714000
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