7:44 Done elementary_linear_algebra_8th_edi... O 31. The set of all 2 × 2 singular matrices 32. The set of all 2 x 2 nonsingular matrices 33. The set of all 2 × 2 diagonal matrices 34. The set of all 3 × 3 upper triangular matrices 35. C[0, 1], the set of all continuous functions defined on the interval [0, 1] 36. C[-1, 1], the set of all continuous functions defined on the interval [-1, 1] 37. Let V be the set of all positive real numbers. Determine whether V is a vector space with the operations shown below. x + y = xy Addition Scalar multiplication Cx = x° If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail. 38. Determine whether the set R² with the operations (x,*2, YıY2) (x1, yı) + (x2, y2) and c(x1, y1) = (cx1, cy,) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail. 39. Proof Prove in full detail that the set {(x, 2x): x is a real number}, with the standard operations in R2, is a vector space. d, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 167 4.2 Exercises standard 46. CAPSTONE (a) Describe the conditions under which a set may be classified as a vector space. addition perations (b) Give an example of a set that is a vector space and an example of a set that is not a vector space.

Q: Evaluate: da

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Q: lim, 2+ f(x) = →2+ lim 2- f(x) =

A: Given query is to find indicated limit.

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Q: (a-5)

A: Solve the (a-5)6

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Q: #2 - Niku

A: Given, The Caesar cipher method to encrypts message by changing each letter of the alphabet to the…

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Q: Suppose that the functions g and fare defined as follows. 8 (x) = (-5 +x)(-5+x) f (x) = -6-8x (f)<s.…

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Q: answer question 2

A: As per the question we are given the following recurrence relation : T(n) = 6T(n/2) + n  ,  T(1) = 1…

Q: Number 28

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Q: (a-5)

A: Given:            (a−5)6

Q: 12 13

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Q: Match the possible graph for the function f with the specified properties: (i) the domain of ƒ is…

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Q: Add. 4 4a + 3

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Q: limx→- f(x) limo+ f(x) limx→ = = =

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A: Given: x5yx4y6

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Q: 12+z=15

A: 12+Z= 15 Z = 15 - 12

Q: (a-5)

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Q: -5/9 + 1/2

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Q: limx→2 f(x) = lim, ¹x→−1+ f(x) =

A: Given graph of the function fx is   1. Find :  limx→2 fx. 2. Find :limx→-1+ fx.

Q: 20 . 35 60.

A: Given equation: 20=3560 Consider the missing term be 'x' 20x=3560 The objective is to find the value…

Q: (a-5)

A: Given :- (a–5)6 Using Formula :- (a–b)3 = a3–b3–3a2b+3ab2

Q: Find x. X+4

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.