We have learned how to simplify, add, subtract, multiply, and divide rational expressions. The procedure for each operation is different, and it takes considerable practice to determine the correct method to apply for a given problem. The following review exercises give you the opportunity to practice the specific techniques for simplifying rational expressions. For Exercises 1–20, perform any indicated operations, and simplify the expression. 3 k − 8 k − 5 + k − 12 k − 5
We have learned how to simplify, add, subtract, multiply, and divide rational expressions. The procedure for each operation is different, and it takes considerable practice to determine the correct method to apply for a given problem. The following review exercises give you the opportunity to practice the specific techniques for simplifying rational expressions. For Exercises 1–20, perform any indicated operations, and simplify the expression. 3 k − 8 k − 5 + k − 12 k − 5
Solution Summary: The author explains the formula used to calculate the sum of the expression, 3k-8k-5+
We have learned how to simplify, add, subtract, multiply, and divide rational expressions. The procedure for each operation is different, and it takes considerable practice to determine the correct method to apply for a given problem. The following review exercises give you the opportunity to practice the specific techniques for simplifying rational expressions.
For Exercises 1–20, perform any indicated operations, and simplify the expression.
Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N
then dim M = dim N but the converse need not to be true.
B: Let A and B two balanced subsets of a linear space X, show that whether An B and
AUB are balanced sets or nor.
Q2: Answer only two
A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists
ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}.
fe
B:Show that every two norms on finite dimension linear space are equivalent
C: Let f be a linear function from a normed space X in to a normed space Y, show that
continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence
(f(x)) converge to (f(x)) in Y.
Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as
normed space
B: Let A be a finite dimension subspace of a Banach space X, show that A is closed.
C: Show that every finite dimension normed space is Banach space.
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
Three streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are
not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of
Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less
than half of the difference between the rates of Stream A and Stream C.
Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x.
Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination
matrix E such that U = E A, provide also the components of E.
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