EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Textbook Question
Chapter 12, Problem 23P
Electrical Engineering
Perform the same computation as in Sec. 12.3, but for the circuit depicted in Fig. P12.23.
FIGURE P12.23
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Your work should be submitted on Moodle, before February 7 at 5 pm.
1. True or false:
(a) if E is a subspace of V, then dim(E) + dim(E) = dim(V)
(b) Let {i, n} be a basis of the vector space V, where v₁,..., Un are all eigen-
vectors for both the matrix A and the matrix B. Then, any eigenvector of A is
an eigenvector of B.
Justify.
2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1,2,-2), (1, −1, 4), (2, 1, 1)}.
3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal
projection onto the orthogonal complement E.
(a) The combinations of projections P+Q and PQ correspond to well-known oper-
ators. What are they? Justify your answer.
(b) Show…
1. True or false:
(a) if E is a subspace of V, then dim(E) + dim(E+) = dim(V)
(b) Let {i, n} be a basis of the vector space V, where vi,..., are all eigen-
vectors for both the matrix A and the matrix B. Then, any eigenvector of A is
an eigenvector of B.
Justify.
2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1, 2, -2), (1, −1, 4), (2, 1, 1)}.
3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal
projection onto the orthogonal complement E.
(a) The combinations of projections P+Q and PQ correspond to well-known oper-
ators. What are they? Justify your answer.
(b) Show that P - Q is its own inverse.
4. Show that the Frobenius product on n x n-matrices,
(A, B) =
= Tr(B*A),
is an inner product, where B* denotes the Hermitian adjoint of B.
5. Show that if A and B are two n x n-matrices for which {1,..., n} is a basis of eigen-
vectors (for both A and B), then AB = BA.
Remark: It is also true that if AB = BA, then there exists a common…
Chapter 12 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 12 - Chemical/Bio Engineering
12.1 Perform the same...Ch. 12 - Chemical/Bio Engineering If the input to reactor 3...Ch. 12 - Chemical/Bio Engineering Because the system shown...Ch. 12 - Chemical/Bio Engineering
12.4 Recompute the...Ch. 12 - Chemical/Bio Engineering Solve the same system as...Ch. 12 - Chemical/Bio Engineering
12.6 Figure P12.6 shows...Ch. 12 - Chemical/Bio Engineering
12.7 Employing the same...Ch. 12 - Chemical/Bio Engineering The Lower Colorado River...Ch. 12 - Chemical/Bio Engineering A stage extraction...Ch. 12 - Chemical/Bio Engineering
12.10 An irreversible,...
Ch. 12 - Chemical/Bio Engineering
12.11 A peristaltic pump...Ch. 12 - Chemical/Bio Engineering
12.12 Figure P12.12...Ch. 12 - Civil/Environmental Engineering A civil engineer...Ch. 12 - Civil/Environmental Engineering Perform the same...Ch. 12 - Civil/Environmental Engineering
12.15 Perform the...Ch. 12 - Civil/Environmental Engineering Calculate the...Ch. 12 - Civil/Environmental Engineering In the example for...Ch. 12 - Civil/Environmental Engineering Employing the same...Ch. 12 - Civil/Environmental Engineering Solve for the...Ch. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Civil/Environmental Engineering
12.22 A truss is...Ch. 12 - Electrical Engineering
12.23 Perform the same...Ch. 12 - Electrical Engineering Perform the same...Ch. 12 - Electrical Engineering
12.25 Solve the circuit in...Ch. 12 - Electrical Engineering
12.26 An electrical...Ch. 12 - Electrical Engineering
12.27 Determine the...Ch. 12 - Electrical Engineering Determine the currents for...Ch. 12 - Electrical Engineering The following system of...Ch. 12 - Electrical Engineering
12.30 The following system...Ch. 12 - Mechanical/Aerospace Engineering Perform the same...Ch. 12 - Mechanical/Aerospace Engineering
12.32 Perform the...Ch. 12 - Mechanical/Aerospace Engineering
12.33 Idealized...Ch. 12 - Mechanical/Aerospace Engineering Three blocks are...Ch. 12 - Mechanical/Aerospace Engineering Perform a...Ch. 12 - Mechanical/Aerospace Engineering Perform the same...Ch. 12 - Mechanical/Aerospace Engineering
12.37 Consider...Ch. 12 - Mechanical/Aerospace Engineering The steady-state...Ch. 12 - Mechanical/Aerospace Engineering
12.40 A rod on a...
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