The height at Point X is determined by levelling from four benchmarks BMA, BMB, BMC and BMD as shown in Figure 1. The observed height differences, the lengths of levelling lines and the heights of benchmarks are recorded in Table 2. The weighted levelling adjustment is considered. , h L L h3 B L3 Figure 1 X=7 h Height of benchmarks HA = 2.315m Height difference Length h = 7.67Xm L = 4km HB = 3.662m Hc=7.93Xm HD -0.77Xm h2=-6.338m h3 = 2.065m h4=-9.235m L2 = 2km L3 = 3km L4=8km Table 2 (a) Construct a system of observation equations to resolve the height of Point X. (4 marks) (b) List the observation equations in matrix form (AX=L+V) and the weight matrix. (5 marks) (c) Compute the normal matrix and find the MOST probable height of Point X. (5 marks) (d) What are the residuals of each of the height differences? (8 marks) (e) Determine the reference standard deviation of this levelling adjustment. (3 marks)