DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<
16th Edition
ISBN: 9781323235911
Author: BITTINGER
Publisher: Pearson Custom Publishing
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Chapter A, Problem 61ES
To determine
To fill: The blank in the statement, “
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1) Compute the inverse of the following matrix.
0
1
1
A =
5
1
-1
2-3
-3
Question 3 (5pt): A chemical reaction. In an elementary chemical reaction,
single molecules of two reactants A and B form a molecule of the product C :
ABC. The law of mass action states that the rate of reaction is proportional
to the product of the concentrations of A and B:
d[C]
dt
= k[A][B]
(where k is a constant positive number). Thus, if the initial concentrations are
[A] =
= a moles/L and [B] = b moles/L we write x = [C], then we have
(E):
dx
dt
=
k(ax)(b-x)
1
(a) Write the differential equation (E) with separate variables, i.e. of the form
f(x)dx = g(t)dt.
(b) Assume first that a b. Show that
1
1
1
1
=
(a - x) (b - x)
-
a) a - x
b - x
b)
(c) Find an antiderivative for the function f(x) = (a-x) (b-x) using the previous
question.
(d) Solve the differentiel equation (E), i.e. find x as a function of t. Use the fact
that the initial concentration of C is 0.
(e) Now assume that a = b. Find x(t) assuming that a = b. How does this
expression for x(t) simplify if it is known that [C] =…
2) Consider the matrix
M
=
[1 2 3 4 5
0 2 3 4 5
00345
0 0 0 4 5
0 0 0 0 5
Determine whether the following statements are True or False.
A) M is invertible.
B) If R5 and Mx = x, then x = 0.
C) The last row of M² is [0 0 0 0 25].
D) M can be transformed into the 5 × 5 identity matrix by a sequence of elementary
row operations.
E) det (M) 120
=
Chapter A Solutions
DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<
Ch. A - Use the unit below to measure the length of each...Ch. A - Prob. 2DECh. A - Prob. 3DECh. A - Prob. 4DECh. A - Prob. 5DECh. A - Prob. 6DECh. A - Prob. 7DECh. A - Prob. 8DECh. A - Prob. 9DECh. A - Prob. 10DE
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