Example SURE 372 Exam Questions

• If A = {xÎR|-4<x<3} and B = { xÎR|-1<x<7} find AÈB, AÇB, and comp (A).

• Using Venn diagrams, show (AÈB)Ç(AÈC) and AÇ(BÈC)

• Find the angle between these two vectors: and .

• What is linear independence?

• What is the difference between Gaussian elimination and Gauss-Jordan reduction?

• Solve the following system of equations using Gaussian elimination and by using matrices

• Put the following matrix into reduced row echelon form

• Define the following terms: trace, banded-bordered matrix, upper triangular matrix.

• If

Find 2A + B; AC; CB.

• Solve the following equations by Cramer's Rule:

• Find the inverse of by Gauss Jordan elimination.

• Find the eignevalues for the following matrix:

• Given , form the LU factorization.

• Find the partial derivatives of the following:

• Given: 27, 29, 22, 23, 25, find the: arithmetic mean, median, standard deviation.

• An azimuth between points A and B is 147^o 31' 50" with a distance of 305.41 m was measured in the field. If the standard deviation of the azimuth is ±5" and the standard deviation in the distance is ±0.06 m, what is the uncertainty in the X and Y coordinates of point B relative to point A?

• A sample mean of 20 independent distance measurements is calculated to be 537.615 m. The sample standard deviation of the same 20 measurements is calculated to be 0.035 m. Construct a 95% confidence interval for the population mean, m.

• A level rod is observed 15 times with a precise level that is equipped with a micrometer. Following are the rod readings (assumed to be a random sample from a normal distribution):

1412.80 mm	1412.85 mm	1412.87 mm
1413.09 mm	1412.50 mm	1412.80 mm
1412.86 mm	1412.84 mm	1412.66 mm
1412.80 mm	1412.84 mm	1412.84 mm
1412.78 mm	1413.02 mm	1412.72 mm

Test the hypothesis H₀: s = 0.08 mm against H₁: s ¹ 0.08 mm at the 5% level of significance.