Let U and W be subspaces of V (a) Show that U + W is a subspace
Question:
(a) Show that U + W is a subspace of V containing U and W.
(b) Show that span {u, w} = Ru + Rw for any vectors u and w.
(c) Show that span {u1,...um, w1...,wn} = span{u1 ..., um} + span{w1 ..., wn} for any vectors ui in U and wj in W.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 76% (13 reviews)
b Observe that Ru su s in R Hen...View the full answer
Answered By
Ashish Bhalla
I have 12 years work experience as Professor for Accounting, Finance and Business related subjects also working as Online Tutor from last 8 years with highly decentralized organizations. I had obtained a B.Com, M.Com, MBA (Finance & Marketing). My research interest areas are Banking Problem & Investment Management. I am highly articulate and effective communicator with excellent team-building and interpersonal skills; work well with individuals at all levels.
4.80+
17+ Reviews
46+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Let U and W be subspaces of V, let dim V = n and assume that dim U + dim W = n. (a) If U W= {0}. show that V = UW. (b) If U+W= V,, show that V = UW. [Hint: Theorem 5 6.4.]
-
Let U and W be subspaces of a finite-dimensional vector space V. Prove Grassmann's Identity: dim ( U + W) = dim U + dim W - dim( U W)
-
Let U and W be subspaces of a finite-dimensional vector space V. Define T: U W V by T(u, w) = u - w. (a) Prove that T is a linear transformation. (b) Show that range(T) = U + W. (c) Show that...
-
machine element is made of an alloy with Yield strength of 200 Mpa and fracture strain is 0.08. A machine element is characterized by the normal stress components as shown in the figure. The Answer...
-
Distinguish between changes that affect consistency and those that may affect comparability but not consistency. Give an example of each.
-
In Problems 1 and 2, y = 1/(1 + c 1 e -x ) is a one-parameter family of solutions of the first-order DE y' = y - y 2 . Find a solution of the first-order IVP consisting of this differential equation...
-
House Handy Products manufactures plastic products and utensils for use in several situations. The company produces and sells a vast range of products that can be used in the home (plastic cooking...
-
One of the more closely watched ratios by investors is the price/earnings or P/E ratio. By dividing price per share by earnings per share, analysts get insight into the value the market attaches to a...
-
Use the given table to find the probability of the indicated event. Round your answer to the nearest thousandth. College students were given three choices of pizza toppings and asked to choose one...
-
Draw the structure of (2Z,5Z)-3-bromohepta-2,5-diene. Br A) B) Br C) D) Br Br
-
Let V be the set of all infinite sequences (a0, a1, a2,...) of real numbers. Define addition and scalar multiplication by (a0, a1,...) + (b0, b1,...) = (a0 + b0, a1 + b1,...) and r(a0, a1,...) =...
-
In each case, find a basis of v containing v and w. (a) V = (R4, v = (0, 0, 1, l),w = (1, 1, 1, 1) (b) V= P3, v = x2 + 1, w = x2 + x
-
This comment appeared in the annual report of MacCloud Inc.: The Company could pay cash or property dividends on the Class A common stock without paying cash or property dividends on the Class B...
-
Mary and Joseph are married with 2 children: Jesse, age 1 5 , and Jessica, age 8 . For the current year, the couple s taxable income is $ 3 0 0 , 0 0 0 . What is their tax credit amount related to...
-
Eddie slick Haskell needs your tax advice regarding a recent stock transaction that didnt turn out the way he planned. On January 20, 2021, Slick purchased 100 shares of Tesla stock (ticker TSLA) for...
-
Inc. settled an overdue account in the amount of $2,000 on January 16 with YYY Company. The customer signed a 30-day promissory note bearing 6% to the lender. What would be the JEs for both companies...
-
Prepare a retained earnings statement. Cash $32,000 Accounts Receivable 1,200 Accounts Payable 3,000 Allowance for Doubtful accounts 200 Common Stock 25,000 Cost of Goods Sold 23,000 Retained...
-
Continuing with Bolt data in the previous problem, assume Bolt budgeted a 10.0% share sales of total bolt products in the local market. Reliable industry data indicates that the actual total number...
-
In Question 2.4, suppose that Arvind is not worried about risk provided that he can cover his costs. If he thinks that the exchange rate will change to 50 INR in 90 days, explain how he could use a...
-
AB CORPORATION ISSUED THE FOLLOWING 850 COMMON STOCKS PAR VALUE P100 750 PARTICIPATING PREFERRED STOCKS PAR VALUE P100 AT 3% AB CORPORATION DECLARED P100,000.00 DIVIDEND IN 2022.
-
Consider the transition matrix (a) Calculate x(n) for n = 1, 2, 3, 4, 5, if (b) State why P is regular and find its steady-state vector. 2 4
-
Find the steady-state vectors of the following regular transition matrices: (a) (b) (c) 1-3 2-3 81 26 19 .74 2 0 1-4 3-4 1-2 0-2 1-3 1-3 1-3
-
Verify that if P is a k k regular transition matrix all of whose row sums are equal to 1, then the entries of its steady-state vector are all equal to 1 / k.
-
If f(x) = x-9 and g(x) = x + 3x, complete parts (a) (f+g)(x)= 2x+3x-9 (Simplify your answer. Do not factor.) (b) (f-g)(x)=-9-3x (Simplify your answer. Do not factor.) 3 (c) (f-g) (Simplify your...
-
Your portfolio which consists of 46% of stock J, and 54% of stock K. J has daily Standard Deviation 3% while K has daily Standard Deviation 4%. The correlation of two stocks is -0.6. What is the 1...
-
Add as indicated. Write all answers in lowest terms. 3 - + 2 X X-7 3X 2 = X-7 (Simplify your answer.)
Study smarter with the SolutionInn App