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Math 332 Test 2 Name: 1. Solve the problem below and put your solution in vector form. Matrix Equation Vector Solution State the null space and explain its significance to the linear solution model. 2. Convert the following numbers from one base to another. Show your work. Convert to base 10 Convert from base 10 to the given base. i) .100100100…2 i) 67.5 to base 2. ii) .ABABAB…16 ii) 18978 to base 16. iii) .(n-1)(n-1)(n-1)…n Math 332 Test 2 Name: 3. In a computer system a byte is a sequence of bits in which each bit may be either a 0 or a 1. For example, in the 8-bit byte representation below each box can house either a 0 or a 1. i) How many base 10 whole numbers can be represented with an 8 bit byte? Show your reasoning. ii) What is the largest base 10 whole number representable by an 8-bit byte? iii) All positive integers in an 8-bit byte must have a 0 in the left most bit. With this in mind, what is the largest positive number representable with 8 binary bits? Show your reasoning. iv) Negative integers are stored in binary by designating the left most bit a “1”, such that a given positive number plus its additive inverse equals 100000000. That is, the add so that 1 is carried “off the byte.” Find the 8 bit binary additive inverses of i) 11112 2) 1010102 4. Consider the ODEIVP dy/dx = X2Y when y(0) =1. a) Derive the analytical solution to the ODEIVP. b) Use the Euler/Trapezoid rule to calculate by hand to find the solution to the first 3 points (Including initial value)for the ODEIVP when the step size H = .5. State both x and y values (3 significant digits). Math 332 Test 2 Name: 5. Below is core code for Simpson Calculate by hand the first two iterations of this numerical integration scheme for y=x2+2, beginning with x=0, using step size H = .5 FOR(J,1,N,1) Y1 -->S X+H -->X Y1 -->T X+H --> X Y1 -->U (S+4*T+U)*H/3 -->B A+B-->A END 6. Create a fractal, unlike what we saw in class and unlike those in the homework. Then show how some fractal measure is found.