%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Scientific notation shorthand % Matlab and other programming languages use a shorthand for scientific notation 4.1 * 10^13 ans = 4.1000e+13 % You can also type that shorthand in directly 4.1e13 ans = 4.1000e+13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % You can save and load scalars, vectors, and matrices to disk as follows A = [1 3; -2 7] A = 1 3 -2 7 save -ascii -double A.asc A % save matrix A to file A.asc clear all % clear all variables from memory load A.asc % load data from file A.asc, store in variable A A A = 1 3 -2 7 B = load('A.asc') % or load data from file A.asc into a variable B B = 1 3 -2 7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % How to solve a linear algebra problem in matlab % % two apples, three lemons, and one pear cost $3.30 % one apple, four lemons, and seven pears cost $8.25 % five apples, two lemons, and one pear cost $5.25 % % what do apples, lemons, and pears cost, each? % Translate this into a system of three equations % % 2x + 3y + 1z = 3.45 % 1x + 4y + 7z = 8.25 % 5x + 2y + 1z = 5.25 % Rewrite that in matrix-vector form % [ 2 3 1 ] [x] [3.30] % [ 1 4 7 ] [y] = [8.25] % [ 5 2 1 ] [z] [5.25] % % A x = b % Now type A and b into Matlab A = [ 2 3 1 ; 1 4 7 ; 5 2 1] A = 2 3 1 1 4 7 5 2 1 b = [3.30 ; 8.25 ; 5.25] b = 3.3000 8.2500 5.2500 % Use Matlab's backslash operator to solve Ax=b for x x = A\b x = 0.75000 0.30000 0.90000 % Thus apples cost $0.75, lemons $0.30, and pears $0.90. % Verify that Ax=b A*x ans = 3.3000 8.2500 5.2500 A*x-b ans = 0 0 0 % yep!