Simple graphics in MATLAB

format short x=[0,0.25,0.5,0.75,1] y=[1,0,1,0,1] x=linspace(0,1,6) y=sin(pi*x) plot(x,y) % ploting the function . The result wont look good. so we create a finer grid. x=linspace(0,1,41); y=sin(pi*x); plot(x,y)

Prove that each of the three row operations is reversible. More precisely, if the matrix B is obtained from A by application of a single row operation, show that there is a single row operation that will transform B back into A.

If we can reverse each row operation individually, then we can reverse a sequence of row operations. The operations that reverse each operation are listed below, using our shorthand notation. Notice how requiring the scalar α to be non-zero makes the second operation reversible. Ri ↔ Rj Ri ↔ Rj αRi , α (not equal to) 0 (1 / α ) Ri αRi + Rj − αRi + Rj

Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum.

Let variables x and y represent two nonnegative numbers. The sum of the two numbers is given to be 9 = x + y , so that y = 9 - x . We wish to MAXIMIZE the PRODUCT P = x y^2 . However, before we differentiate the right-hand side, we will write it as a function of x only. Substitute for y getting P = x y^2 = x ( 9-x)^2 . Now differentiate this equation using the product rule and chain rule, getting P' = x (2) ( 9-x)(-1) + (1) ( 9-x)^2 = ( 9-x) [ -2x + ( 9-x) ] = ( 9-x) [ 9-3x ] = ( 9-x) (3)[ 3-x ] = 0 for x=9 or x=3 . If x=3 and y=6 ,then P= 108