Begin2.DVI

10-9. Assume that Ais a square matrix show that (a)AA T is symmetric (b)A+AT is symmetric (c)A−AT is skew-symmetric (d) Show Ac ...

10-17. Background material Definition: (Congruence) Two integers I and J are said to be congruent modulo L,(written I≡J(mod L)) ...

there results B=AC =   8 15 23 1 18 5 25 15 21     1 1 0 0 1 − 1 1 −2 4  =   2 6 19 6 9 2 17 27 11  =   B F S F I ...

10-18. Evaluate the following determinants: (a) ∣∣ ∣∣3 2 4 − 1 ∣∣ ∣∣ (b) ∣∣ ∣∣ 0 3 −2 0 ∣∣ ∣∣ (c) ∣∣ ∣∣1 2 3 4 ∣∣ ∣∣
10-19. Ev ...

10-24. Let A= [ 4 3 −1 0 ] B= [ −1 1 2 − 3 ] (a) Calculate C=AB (b) Find |A|, |B|, |C| (c) Verify that |C|=|A||B|
10-25. Show ...

10-30. Let A= [ a 11 a 12 a 21 a 22 ] , where aij =aij(t), i, j = 1, 2 , 3 are differentiable functions of t. (a) Show d dt (de ...

10-34. Let A= [ t^3 +t cos 3 t e^4 t tanh2t ] and find (a) dA dt (b) ∫ A dt
10-35. Let C(λ) = |A−λI |=det (A−λI ) = 0 denote t ...

10-39. Show the relation between the vector differential equation d ̄y dt =A(t) ̄y+ f ̄(t), y ̄(0) = ̄c and the matrix differen ...

Chapter 11 Introduction to Probability and Statistics The collecting of some type of data, organizing the data, determining how ...

(v) Finding ways to improve the system by experimenting with how inputs and parameter values produce changes in the system. (vi) ...

Some examples of discrete data is presented in the table 11.1. These numbers can be plotted as vertical or horizontal bar graphs ...

127 115 132 117 138 138 152 121 142 120 104 116 139 165 150 132 142 94 124 145 157 137 118 163 138 159 140 87 162 132 156 148 15 ...

Table 11.3 Frequency Table Cumulative Class Class Relative Cumulative Relative Interval Midpoint Tallies Frequency Frequency Fre ...

Figure 11-3. The relative frequency function and cumulative relative frequency function The results illustrated in the table 11. ...

Also define a cumulative frequency function F(x)for the sample, sometimes re- ferred to as a sample distribution function. The c ...

quartiles. Note that Q 2 will be the same as the median. If the data set is divided into ten equal parts by numbers D 1 , D 2 , ...

and for a continuous set of values f(x)over an interval (a, b)it is defined RMS = √ 1 b−a ∫b a [f(x)]^2 dx (11.9) The root mean ...

there will be very little difference in calculation of the standard deviation from either definition. To convert the standard de ...

In general, if the true population mean μis known exactly , so that μ=^1 N ∑N j=1 Xj, where N is the population size, then the p ...

denoted by A∩B=∅. In this case, the sets Aand Bare said to be mutually exclusive events or disjoint events. The notation A⊂Bis u ...