Mathematics, 24.06.2020 21:01 sophoyak

Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) To show that a set is not a vector space, it is sufficient to show that just one axiom is not satisfied.
1. True, for a set with two operations to be a vector space all 10 axioms must be satisfied. Therefore, if just one of the axioms fails, then this set cannot be a vector space.
2. False, for a set with two operations to be a vector space a majority of 10 axioms must be satisfied. Therefore, if just one of the axioms fails, then this set can still be a vector space.
3. False, for a set with two operations to be a vector space at least one of the 10 axioms must be satisfied. Therefore, if just one of the axioms fails, then this set can still be a vector space.
4. False, for a set with two operations to be a vector space at least 9 of the 10 axioms must be satisfied. Therefore, if just one of the axioms fails, then this set can still be a vector space.
5. False, for a set with two operations to be a vector space at least 8 of the 10 axioms must be satisfied. Therefore, if just one of the axioms fails, then this set can still be a vector space.
(b) The set of all first-degree polynomials with the standard operations is a vector space.
1. True. The set is a vector space because all 10 axioms are satisfied.
2. False. The set is not a vector space because it is not closed under addition.
3. False. The set is not a vector space because it does not have the commutative property of addition.
4. False. The set is not a vector space because it does not have the associative property of addition.
5. False. The set is not a vector space because a scalar identity does not exist.
(c) The set of all pairs of real numbers of the form (0, y), with the standard operations on R^2, is a vector space.
1. True. The set is a vector space because all 10 axioms are satisfied.
2. False. The set is not a vector space because it is not closed under addition.
3. False. The set is not a vector space because an additive inverse does not exist.
4. False. The set is not a vector space because it is not closed under scalar multiplication.
5. False. The set is not a vector space because a scalar identity does not exist.

Answers: 3

Show answers

Another question on Mathematics

Mathematics, 21.06.2019 19:00

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

(i really need ) read the story problem, and then answer the questions that follow. gordon works for a graphic design firm and is creating a label for a food truck vendor. the vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. to complete his label, gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches. part a: find the slant height of the cone. the slant height is the distance from the apex, or tip, to the base along the cone’s lateral surface. show your work. part b: find the measure of the angle formed between the base of the cone and a line segment that represents the slant height. part c: imagine two line segments where each represents a slant height of the cone. the segments are on opposite sides of the cone and meet at the apex. find the measurement of the angle formed between the line segments.

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

The weight of 46 new patients of a clinic from the year 2018 are recorded and listed below. construct a frequency distribution, using 7 classes. then, draw a histogram, a frequency polygon, and an ogive for the data, using the relative information from the frequency table for each of the graphs. describe the shape of the histogram. data set: 130 192 145 97 100 122 210 132 107 95 210 128 193 208 118 196 130 178 187 240 90 126 98 194 115 212 110 225 187 133 220 218 110 104 201 120 183 124 261 270 108 160 203 210 191 180 1) complete the frequency distribution table below (add as many rows as needed): - class limits - class boundaries - midpoint - frequency - cumulative frequency 2) histogram 3) frequency polygon 4) ogive

Answers: 1

Answer

Mathematics, 22.06.2019 03:40

Amanufacturer knows that their items have a normally distributed lifespan, with a mean if 9.1 years, and standard deviation of 2.9 years. if you randomly purchase one item, what is the probability it will last longer than 10 years?

Answers: 3

Answer

You know the right answer?

Determine whether each statement is true or false. If a statement is true, give a reason or cite an...

Questions