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1. Recall the definition of a skew-symmetric n×n matrix from Homework1: a matrix A is skew-symmetric if A = -At. Then the subset Wn ⊂Mn×n(R) of skew-symmetric n×n real matrices is a real vector space (asyou already knew if you answered that homework question correctly).In particular, consider the subspace W3 ⊂ M3×3(R) of skew-symmetric3 × 3 matrices.(a) Find a basis for W3(b) Use your basis to find the dimension of W37. Suppose S is a subset of a vector space V .(a) Show that if v ∈ V is contained in span(S), then span(S ∪ {v}) =span(S).(b) Show that if v ∈ V is not contained in span(S), thendim(span(S ∪ {v})) = dim(span(S)) + 1
2. Suppose S is a subset of a vector space V .(a) Show that if v ∈ V is contained in span(S), then span(S ∪ {v}) =span(S).(b) Show that if v ∈ V is not contained in span(S), thendim(span(S ∪ {v})) = dim(span(S)) + 1.
1. A chemistry teacher needs to mix a 30% salt solution with a 70% salt solution to make 20 qt of a 40% salt solution. How many quarts of each solution should the teacher mix to get the desired result?
Find the closure of the set {Instructor, Grade} in School. - Show that X is a super key if and only if X+ is the set of all attributes of R. Hint! For "if " construct X+ step by step.
Poker, in the deck 52 cards, hand of 5 cards, one of the winning hands is flush, all cards belong to a common suit. A) Calculate the number of possible combinations of poker hands B) Calculate a probabilty of flush
A small gift shop is trying to determine the number of gift items it can sell to maintain a monthly revenue greater than $10,000. The revenue function for this business is R = -0.10N2 +70N, where R=monthly revenue and N=number of gift items sold p..
use this distribution for finding confidence intervals for the population mean when the sample size is less than 30 and
with end of month contributions of 251.33 an investment account is expected reach 100000 in value after 15 years and 5
As part of his retirement planning, Mr. Martin purchases an annuity that pays 8.5% compounded semiannually. If the semiannual payment is $9,500, how much will Mr. Martin have saved in 4 years?
a body at an unknown temperature 'y' is placed in a room which is held in a room which is held at a constant temperature of 30'F. if after 10 minutes the temperature of the body is 0'F and after 20minutes the temperature of the body is 15'F, find ..
Let f be a real-valued continuous function. Recall that for any subset S ⊆ R, then f(S) is defined as {f(x) : x ∈ S}. Suppose that f(I) is open for any open interval I. Prove that f is monotonic
An employee is complaining to you about his supervisor. He says that the supervisor expects more from him than from other employees. He feels the supervisor picks on him and gives him the most difficult jobs to do. He is quite unhappy and is consi..
Sample final questions. For each power series, determine its radius of convergence R. By considering the series at x = ±R, determine the exact interval of convergence
Two rainstorms occurred in one week in a certain area. In the first storm 25ml of rain fell per hour, and in the second storm 20ml of rain fell per hour. Rain fell that week for a total of 75 hours for a total rainfall of 1700ml.
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