Consider a (binary) floating point system of the form where . Calculate the relative error, with respect to -norm if we convert the vector to the given floating point system. When converting to floating point, first convert to a binary number then truncate any additional bits. Note: We are interested in the representation accuracy of floating point. So assume that all operations performed (addition, subtraction, etc.) do not increase the error.

In a heat transfer course, we can derive the equation for the temperature distribution in a flat rectangular plate. in this example, we will look at a plate at steadystate with three sides being held at t1, and one side held at t2. the temperature for any location on the plate, t(x,y), can be calculated by where create a function (prob3_5) that will take inputs of vectors x and y in feet, scalar n, scalars l and w in feet and scalars t1 and t2 in degrees fahrenheit. it will output a matrix t which is the temperature of each x and y locations. t will have the number of columns equal to the number of elements in x and rows equal to the number of elements in y. though this can be done without loops (perhaps more efficiently), your program must use a nested loop.