Elementary Differential Equations
10th Edition
ISBN: 9780470458327
Author: William E. Boyce, Richard C. DiPrima
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2.6, Problem 27P
To determine
The integrating factor and solve the equation
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of 2
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The set of all 3 x 3 upper triangular matrices
6) Determine whether each of the following sets, together with the standard
operations, is a vector space. If it is, then simply write 'Vector space'. You do not
have to prove all ten vector space axioms. If it is not, then identify one of the ten
vector space axioms with its number in the attached sheet that fails and also show
that how it fails.
a) The set of all polynomials of degree four or less.
b) The set of all 2 x 2 singular matrices.
c) The set {(x, y) : x ≥ 0, y is a real number}.
d) C[0,1], the set of all continuous functions defined on the interval [0,1].
7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and
show that it is orthogonal to both u and v.
8) a) Find the equation of the least squares regression line for the data points
below.
(-2,0), (0,2), (2,2)
b) Graph the points and the line that you found from a) on the same Cartesian
coordinate plane.
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1
of 2
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ZOOM +
1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
Please help solve the following whilst showing all working out. Is part of exam revision questions but no solution is given
Chapter 2 Solutions
Elementary Differential Equations
Ch. 2.1 - In each of Problems 1 through 12:
Draw a direction...Ch. 2.1 - In each of Problems 1 through 12:
Draw a direction...Ch. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.1 - Prob. 5PCh. 2.1 - Prob. 6PCh. 2.1 - In each of Problems 1 through 12:
Draw a direction...Ch. 2.1 - Prob. 8PCh. 2.1 - Prob. 9PCh. 2.1 - Prob. 10P
Ch. 2.1 - In each of Problems 1 through 12:
Draw a direction...Ch. 2.1 - In each of Problems 1 through 12:
Draw a direction...Ch. 2.1 - Prob. 13PCh. 2.1 - Prob. 14PCh. 2.1 - In each of Problems 13 through 20, find the...Ch. 2.1 - Prob. 16PCh. 2.1 - Prob. 17PCh. 2.1 - Prob. 18PCh. 2.1 - In each of Problems 13 through 20, find the...Ch. 2.1 - Prob. 20PCh. 2.1 - In each of Problems 21 through 23:
Draw a...Ch. 2.1 - In each of Problems 21 through 23:
Draw a...Ch. 2.1 - In each of Problems 21 through 23:
Draw a...Ch. 2.1 - Prob. 24PCh. 2.1 - Prob. 25PCh. 2.1 - Prob. 26PCh. 2.1 - Prob. 27PCh. 2.1 - Prob. 28PCh. 2.1 - Consider the initial value problem
Find the...Ch. 2.1 - Prob. 30PCh. 2.1 - Prob. 31PCh. 2.1 - Show that all solutions of 2y′ + ty = 2 [Eq. (41)...Ch. 2.1 - Show that if a and λ are positive constants, and b...Ch. 2.1 - Prob. 34PCh. 2.1 - Prob. 35PCh. 2.1 - Prob. 36PCh. 2.1 - Prob. 37PCh. 2.1 - Prob. 38PCh. 2.1 - Prob. 39PCh. 2.1 - Prob. 40PCh. 2.1 - Prob. 41PCh. 2.1 - Prob. 42PCh. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 1 through 8, solve the given...Ch. 2.2 - In each of Problems 9 through 20:
Find the...Ch. 2.2 - Prob. 10PCh. 2.2 - In each of Problems 9 through 20:
Find the...Ch. 2.2 - Prob. 12PCh. 2.2 - Prob. 13PCh. 2.2 - Prob. 14PCh. 2.2 - In each of Problems 9 through 20:
Find the...Ch. 2.2 - Prob. 16PCh. 2.2 - In each of Problems 9 through 20:
Find the...Ch. 2.2 - In each of Problems 9 through 20:
Find the...Ch. 2.2 - Prob. 19PCh. 2.2 - Prob. 20PCh. 2.2 - Prob. 21PCh. 2.2 - Prob. 22PCh. 2.2 - Prob. 23PCh. 2.2 - Solve the initial value problem
y′ = (2 − ex)/(3 +...Ch. 2.2 - Prob. 25PCh. 2.2 - Prob. 26PCh. 2.2 - Prob. 27PCh. 2.2 - Prob. 28PCh. 2.2 - Prob. 29PCh. 2.2 - Prob. 30PCh. 2.2 - Prob. 31PCh. 2.2 - The method outlined in Problem 30 can be used for...Ch. 2.2 - Prob. 33PCh. 2.2 - Prob. 34PCh. 2.2 - The method outlined in Problem 30 can be used for...Ch. 2.2 - The method outlined in Problem 30 can be used for...Ch. 2.2 - The method outlined in Problem 30 can be used for...Ch. 2.2 - The method outlined in Problem 30 can be used for...Ch. 2.3 - Consider a tank used in certain hydrodynamic...Ch. 2.3 - A tank initially contains 120 L of pure water. A...Ch. 2.3 - A tank originally contains 100 gal of fresh water....Ch. 2.3 - A tank with a capacity of 500 gal originally...Ch. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - Prob. 9PCh. 2.3 - A home buyer can afford to spend no more than...Ch. 2.3 - A home buyer wishes to borrow $250,000 at an...Ch. 2.3 - A recent college graduate borrows $150,000 at an...Ch. 2.3 - An important tool in archeological research is...Ch. 2.3 - Suppose that a certain population has a growth...Ch. 2.3 - Suppose that a certain population satisfies the...Ch. 2.3 - Newton’s law of cooling states that the...Ch. 2.3 - Prob. 17PCh. 2.3 - Prob. 18PCh. 2.3 - Prob. 19PCh. 2.3 - A ball with mass 0.15 kg is thrown upward with...Ch. 2.3 - Assume that the conditions are as in Problem 20...Ch. 2.3 - Prob. 22PCh. 2.3 - Prob. 23PCh. 2.3 - Prob. 24PCh. 2.3 - Prob. 25PCh. 2.3 - Prob. 26PCh. 2.3 - Prob. 27PCh. 2.3 - Prob. 28PCh. 2.3 - Prob. 29PCh. 2.3 - Prob. 30PCh. 2.3 - Prob. 31PCh. 2.3 - Prob. 32PCh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.4 - Prob. 10PCh. 2.4 - Prob. 11PCh. 2.4 - Prob. 12PCh. 2.4 - Prob. 13PCh. 2.4 - Prob. 14PCh. 2.4 - Prob. 15PCh. 2.4 - Prob. 16PCh. 2.4 - Prob. 17PCh. 2.4 - Prob. 18PCh. 2.4 - Prob. 19PCh. 2.4 - Prob. 20PCh. 2.4 - Prob. 21PCh. 2.4 - Prob. 22PCh. 2.4 - Prob. 23PCh. 2.4 - Prob. 24PCh. 2.4 - Prob. 25PCh. 2.4 - Prob. 26PCh. 2.4 - Prob. 27PCh. 2.4 - Prob. 28PCh. 2.4 - Prob. 29PCh. 2.4 - Prob. 30PCh. 2.4 - Prob. 31PCh. 2.4 - Prob. 32PCh. 2.4 - Prob. 33PCh. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10PCh. 2.5 - Prob. 11PCh. 2.5 - Prob. 12PCh. 2.5 - Prob. 13PCh. 2.5 - Prob. 14PCh. 2.5 - Prob. 15PCh. 2.5 - Prob. 16PCh. 2.5 - Prob. 17PCh. 2.5 - Prob. 18PCh. 2.5 - Prob. 19PCh. 2.5 - Prob. 20PCh. 2.5 - Prob. 21PCh. 2.5 - Prob. 22PCh. 2.5 - Prob. 23PCh. 2.5 - Prob. 24PCh. 2.5 - Prob. 25PCh. 2.5 - Prob. 26PCh. 2.5 - Prob. 27PCh. 2.5 - Prob. 28PCh. 2.6 - Determine whether each of the equations in...Ch. 2.6 - Prob. 2PCh. 2.6 - Prob. 3PCh. 2.6 - Determine whether each of the equations in...Ch. 2.6 - Prob. 5PCh. 2.6 - Prob. 6PCh. 2.6 - Prob. 7PCh. 2.6 - Prob. 8PCh. 2.6 - Prob. 9PCh. 2.6 - Prob. 10PCh. 2.6 - Determine whether each of the equations in...Ch. 2.6 - Determine whether each of the equations in...Ch. 2.6 - Prob. 13PCh. 2.6 - Prob. 14PCh. 2.6 - Prob. 15PCh. 2.6 - Prob. 16PCh. 2.6 - Prob. 17PCh. 2.6 - Prob. 18PCh. 2.6 - Prob. 19PCh. 2.6 - Prob. 20PCh. 2.6 - Prob. 21PCh. 2.6 - Prob. 22PCh. 2.6 - Prob. 23PCh. 2.6 - Show that if (Nx – My)/(xM – yN) = R, where R...Ch. 2.6 - In each of Problems 25 through 31, find an...Ch. 2.6 - In each of Problems 25 through 31, find an...Ch. 2.6 - Prob. 27PCh. 2.6 - Prob. 28PCh. 2.6 - Prob. 29PCh. 2.6 - In each of Problems 25 through 31, find an...Ch. 2.6 - In each of Problems 25 through 31, find an...Ch. 2.6 - Prob. 32PCh. 2.7 - In each of Problems 1 through 4:
Find approximate...Ch. 2.7 - Prob. 2PCh. 2.7 - In each of Problems 1 through 4:
Find approximate...Ch. 2.7 - Prob. 4PCh. 2.7 - In each of Problems 5 through 10, draw a direction...Ch. 2.7 - Prob. 6PCh. 2.7 - Prob. 7PCh. 2.7 - Prob. 8PCh. 2.7 - Prob. 9PCh. 2.7 - Prob. 10PCh. 2.7 - Prob. 11PCh. 2.7 - Prob. 12PCh. 2.7 - Prob. 13PCh. 2.7 - Prob. 14PCh. 2.7 - Prob. 15PCh. 2.7 - Prob. 16PCh. 2.7 - Prob. 17PCh. 2.7 - Prob. 18PCh. 2.7 - Prob. 19PCh. 2.7 - Convergence of Euler’s Method. It can be shown...Ch. 2.7 - Prob. 21PCh. 2.7 - Prob. 22PCh. 2.7 - Prob. 23PCh. 2.8 - Prob. 1PCh. 2.8 - Prob. 2PCh. 2.8 - Prob. 3PCh. 2.8 - Prob. 4PCh. 2.8 - Prob. 5PCh. 2.8 - Prob. 6PCh. 2.8 - Prob. 7PCh. 2.8 - Prob. 8PCh. 2.8 - Prob. 9PCh. 2.8 - Prob. 10PCh. 2.8 - Prob. 11PCh. 2.8 - Prob. 12PCh. 2.8 - Prob. 13PCh. 2.8 - Prob. 14PCh. 2.8 - Prob. 15PCh. 2.8 - Prob. 16PCh. 2.8 - Prob. 17PCh. 2.8 - Prob. 18PCh. 2.8 - Prob. 19PCh. 2.9 - Prob. 1PCh. 2.9 - Prob. 2PCh. 2.9 - Prob. 3PCh. 2.9 - Prob. 4PCh. 2.9 - Prob. 5PCh. 2.9 - Prob. 6PCh. 2.9 - Find the effective annual yield of a bank account...Ch. 2.9 - An investor deposits $1000 in an account paying...Ch. 2.9 - A certain college graduate borrows $8000 to buy a...Ch. 2.9 - Prob. 10PCh. 2.9 - Prob. 11PCh. 2.9 - Prob. 12PCh. 2.9 - Prob. 13PCh. 2.9 - Prob. 14PCh. 2 - Prob. 1MPCh. 2 - Prob. 2MPCh. 2 - In each of Problems 1 through 32, solve the given...Ch. 2 - Prob. 4MPCh. 2 - Prob. 5MPCh. 2 - Prob. 6MPCh. 2 - Prob. 7MPCh. 2 - Prob. 8MPCh. 2 - Prob. 9MPCh. 2 - Prob. 10MPCh. 2 - Prob. 11MPCh. 2 - Prob. 12MPCh. 2 - Prob. 13MPCh. 2 - Prob. 14MPCh. 2 - Prob. 15MPCh. 2 - Prob. 16MPCh. 2 - Prob. 17MPCh. 2 - Prob. 18MPCh. 2 - Prob. 19MPCh. 2 - Prob. 20MPCh. 2 - Prob. 21MPCh. 2 - Prob. 22MPCh. 2 - Prob. 23MPCh. 2 - Prob. 24MPCh. 2 - Prob. 25MPCh. 2 - Prob. 26MPCh. 2 - Prob. 27MPCh. 2 - Prob. 28MPCh. 2 - Prob. 29MPCh. 2 - Prob. 30MPCh. 2 - Prob. 31MPCh. 2 - Prob. 32MPCh. 2 - Prob. 33MPCh. 2 - Prob. 34MPCh. 2 - Prob. 35MPCh. 2 - Prob. 36MPCh. 2 - Prob. 37MPCh. 2 - Prob. 38MPCh. 2 - Prob. 39MPCh. 2 - Prob. 40MPCh. 2 - Prob. 41MPCh. 2 - Prob. 42MPCh. 2 - Prob. 43MPCh. 2 - Prob. 44MPCh. 2 - Prob. 45MPCh. 2 - Prob. 46MPCh. 2 - Prob. 47MPCh. 2 - Prob. 48MPCh. 2 - Prob. 49MPCh. 2 - Prob. 50MPCh. 2 - Prob. 51MP
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