 10.5.1: In 1 and 2, use (3) to compute <1'1 and eAt. A = G )
 10.5.2: In 1 and 2, use (3) to compute <1'1 and eAt. A = ( )
 10.5.3: In 3 and 4, use (3) to compute <1'1A = ( )
 10.5.4: In 3 and 4, use (3) to compute <1'1A = ( 0 2 2 2 5 1
 10.5.5: In 58, use (1) and the results in 14 to find the general solution...
 10.5.6: In 58, use (1) and the results in 14 to find the general solution...
 10.5.7: In 58, use (1) and the results in 14 to find the general solution...
 10.5.8: In 58, use (1) and the results in 14 to find the general solution...
 10.5.9: In 912, use (6) to find the general solution of the 2 2 2 5 1 I...
 10.5.10: In 912, use (6) to find the general solution of the 2 2 2 5 1 I...
 10.5.11: In 912, use (6) to find the general solution of the 2 2 2 5 1 I...
 10.5.12: In 912, use (6) to find the general solution of the 2 2 2 5 1 I...
 10.5.13: Solve the system in subject to the initial condition X(O) (:)
 10.5.14: Solve the system in subject to the initial condition X(O) = (:).
 10.5.15: In 1518, use the method of Example 1 to compute t/'1 for the coeff...
 10.5.16: In 1518, use the method of Example 1 to compute t/'1 for the coeff...
 10.5.17: In 1518, use the method of Example 1 to compute t/'1 for the coeff...
 10.5.18: In 1518, use the method of Example 1 to compute t/'1 for the coeff...
 10.5.19: In 1922, use the method of Example 2 to compute eA1 for the coeffi...
 10.5.20: In 1922, use the method of Example 2 to compute eA1 for the coeffi...
 10.5.21: In 1922, use the method of Example 2 to compute eA1 for the coeffi...
 10.5.22: In 1922, use the method of Example 2 to compute eA1 for the coeffi...
 10.5.23: If the matrix A can be diagonalized, then p1 AP = D or A = PDP1 U...
 10.5.24: UseD c 0 ) and (3) to show that Dt = e>..,.t e Dt = e>..,.t
 10.5.25: In 25 and 26, use the results of 23 and 24 to solve the given syste...
 10.5.26: In 25 and 26, use the results of 23 and 24 to solve the given syste...
 10.5.27: (a) Use (1) to fmd the general solution ofX' = G ) X. Use a CAS to ...
 10.5.28: Use (1) to find the general solution of c 0 6 ) X'= 0 5 0 1 0 1 ...
 10.5.29: Reread the discussion leading to the result given in (8). Does the ...
 10.5.30: In Exercises 8.9 we saw that a nonzero n X n matrix A is nilpotent ...
Solutions for Chapter 10.5: Matrix Exponential
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 10.5: Matrix Exponential
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Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Analytic study
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

Bayesâ€™ estimator
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

Bivariate normal distribution
The joint distribution of two normal random variables

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

Center line
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

Conidence level
Another term for the conidence coeficient.

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Critical value(s)
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

Error propagation
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

Experiment
A series of tests in which changes are made to the system under study

Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

Factorial experiment
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Fraction defective control chart
See P chart

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.