 8.4.1E: In 1 and 2 use (3) to compute eAt and eAt. Reference : Equation 3
 8.4.2E: In 1 and 2 use (3) to compute eAt and eAt. Reference : Equation 3
 8.4.3E: In 3 and 4 use (3) to compute eAt. Reference : Equation 3
 8.4.4E: In 3 and 4 use (3) to compute eAt. Reference : Equation 3
 8.4.5E: In 5–8 use (1) to find the general solution of the given system. Re...
 8.4.6E: In 5–8 use (1) to find the general solution of the given system. Re...
 8.4.7E: In 5–8 use (1) to find the general solution of the given system. Re...
 8.4.8E: In 5–8 use (1) to find the general solution of the given system. Re...
 8.4.9E: In 9–12 use (5) to find the general solution of the given system. R...
 8.4.10E: In 9–12 use (5) to find the general solution of the given system. R...
 8.4.11E: In 9–12 use (5) to find the general solution of the given system. R...
 8.4.12E: In 9–12 use (5) to find the general solution of the given system. R...
 8.4.13E: Solve the system in subject to the initial condition Reference : In...
 8.4.14E: Solve the system in subject to the initial condition Reference : In...
 8.4.15E: In 15–18 use the method of Example 1 to compute eAt for the coeffic...
 8.4.16E: In 15–18 use the method of Example 1 to compute eAt for the coeffic...
 8.4.17E: In 15–18 use the method of Example 1 to compute eAt for the coeffic...
 8.4.18E: In 15–18 use the method of Example 1 to compute eAt for the coeffic...
 8.4.19E: In 19 and 20 verify the foregoing result for the given matrix.
 8.4.20E: In 19 and 20 verify the foregoing result for the given matrix.
 8.4.21E: Suppose A = PDP1, where D is defined as in (9). Use (3) to show th...
 8.4.22E: If D is defined as in (9), then find eDt .(reference 9)
 8.4.23E: In 23 and 24 use the results of 19–22 to solve the given system. Re...
 8.4.24E: In 23 and 24 use the results of 19–22 to solve the given system. Re...
 8.4.25E: Reread the discussion leading to the result given in (7). Does the ...
 8.4.26E: A matrix A is said to be nilpotent if there exists some integer m s...
 8.4.27E: Referenc e: Equation 1
 8.4.28E: Use (1) to find the general solution of Use MATLAB or a CAS to find...
Solutions for Chapter 8.4: A First Course in Differential Equations with Modeling Applications 10th Edition
Full solutions for A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
Solutions for Chapter 8.4
Get Full SolutionsThis textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Since 28 problems in chapter 8.4 have been answered, more than 44161 students have viewed full stepbystep solutions from this chapter. Chapter 8.4 includes 28 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052.

Anchor
See Mathematical induction.

Direction vector for a line
A vector in the direction of a line in threedimensional space

Distance (on a number line)
The distance between real numbers a and b, or a  b

Division
a b = aa 1 b b, b Z 0

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Natural exponential function
The function ƒ1x2 = ex.

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Present value of an annuity T
he net amount of your money put into an annuity.

Product of complex numbers
(a + bi)(c + di) = (ac  bd) + (ad + bc)i

Quantitative variable
A variable (in statistics) that takes on numerical values for a characteristic being measured.

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Scalar
A real number.

Scatter plot
A plot of all the ordered pairs of a twovariable data set on a coordinate plane.

Slopeintercept form (of a line)
y = mx + b

Triangular form
A special form for a system of linear equations that facilitates finding the solution.

Unbounded interval
An interval that extends to ? or ? (or both).

Yscl
The scale of the tick marks on the yaxis in a viewing window.