The kernel of L .

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Answer 1

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Chapter 4, Problem 3CTB

a.

To determine

To find:The kernel of L .

b.

To determine

To find:The L(S) .

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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.

Answer 2

Question

Chapter 4, Problem 3CTB

a.

To determine

To find:The kernel of L .

b.

To determine

To find:The L(S) .

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 4, Problem 3CTB

a.

To determine

To find:The kernel of L .

b.

To determine

To find:The L(S) .

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 4, Problem 3CTB

a.

To determine

To find:The kernel of L .

b.

To determine

To find:The L(S) .

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 4, Problem 3CTB

a.

To determine

To find:The kernel of L .

b.

To determine

To find:The L(S) .

Answer 6

Chapter 4, Problem 3CTB

a.

To determine

To find:The kernel of L .

Answer 7

Chapter 4, Problem 3CTB

a.

To determine

To find:The kernel of L .

Answer 8

b.

To determine

To find:The L(S) .

Answer 9

b.

To determine

To find:The L(S) .

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 4.1 - Show that each of the following are linear...Ch. 4.1 - Let L be the linear operator on 2 defined by...Ch. 4.1 - Let a be a fixed nonzero vector in 2 . A mapping...Ch. 4.1 - Let L: 22 be a linear operator. If...Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - Let C be a fixed nn matrix. Determine whether the...Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - For each fC[0,1] , define L(f)=F , where F(x)= 0...

The kernel of L .

Solution Summary: The author explains how to find the kernel of L.

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To find:The kernel of L .

To find:The L(S) .

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Chapter 4 Solutions