Prove Theorem 5 9(d) d If W span(w 1 , , w k ), then v is in W if and only if v w i 0 for all i 1, , k ...

Prove Theorem 5.9(d). d. If W = span(w 1 , . . . , w k ),

Question:

Prove Theorem 5.9(d).

d. If W = span(w₁, . . . , w_k), then v is in W^⊥ if and only if v · w_i = 0 for all i 1, . . . , k.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-0538735452

3rd edition

Authors: David Poole

See More Books

Question Posted: Nov 13, 2018 12:20 PM

See More Questions

Prove Theorem 5.9(c). c. W W = {0}
Prove Theorem 5.9. If f: A -> B, g: B -> C are invertible functions, then g o f: A -> C is invertible and (g 0 f)-1 = f-1 g-1.
Prove Theorem 6.3.5. Let W be a finite-dimensional subspace of an inner product space V. If (v1, v2,. . . . vr) is an orthonormal basis for W, and u is any vector in V, then ++ (u, v,)V, projwu = (u,...
Using the following uniform density curve, answer the question. Plx) 125 7 8 What is the probability that the random variable has a value less than 5? 0.125 0.625 K0.75 0.5
Why don't monopolists try to establish the highest price possible, as many people allege? What would happen to sales? To profits?
ES Do It! Review 7-6 Gator Corporation manufactures several types of accessories. For the year, the gloves and mittens line had sales of $489,000, variable expenses of $360,000, and fixed expenses of...
According to the Observatory of Economic Complexity (OEC), Australia exports 152 products that display the characteristics of comparative advantage. The OEC defines this in slightly different terms...
Presley, Inc., produces two products, ups and downs, in a single process. The joint costs of this process were $42,000, and 39,000 units of ups and 21,000 units of downs were produced. Separable...
A company just paid out an annual dividend of $4. If the dividend will grow at an annual rate of 20% for the next three years only, and at 5% thereafter, what should be the stock price today? Assume...
Henry's Hardware is a small family business in Sacramento, California. The owners, Henry and Kathleen, must use even' square foot of store space as profitably as possible. They have never kept dewed...
Find the orthogonal decomposition of v with respect to W. 2 -1 W = span| .3
Let W be a subspace of R n and v a vector in R n . Suppose that w and w are orthogonal vectors with w in W and that v = w + w. Is it necessarily true that w is in W ? Either prove that it is true or...
Why and when is it essential to calculate a unit cost?
Listed below are pulse rates (beats per minute) from samples of adult males and females. Does there appear to be a difference? Find the coefficient of variation for each of the two samples; then...
When the price of an item goes down, people buy more of it because at a lower price Options: -some new people may be willing to enter the market. -the item is more valuable. -the marginal cost is...
2. Find the sum of the following sequences (3 points) a) 1, 2, 3, 4, 5, 150 ... b) 1, 3, 5, 7, 9, ..., 99 c) -4, 1, 6, 11, 16, 21, . 201 ...
Solving for Rates What annual rate of return is implied on a $2,600 loan taken next year when $6,300 must be repaid in year 12?
Significant Values. In Exercises 9-12, use the range rule of thumb to identify (a) the values that are significantly low, (b) the values that are significantly high, and (c) the values that are...
Use Equation 8-69 to plot an accurate graph of n FD (E) /V for electrons whose Fermi energy is 4.8 eV from E = 4.5 eV to E = 5.1 eV at T = 300 K. Determine from the graph the number of electrons per...
Cornell and Roberts are partners who agree to admit Stanley to their partnership. Cornell has a capital balance of $80,000 and Roberts has a capital balance of $120,000. Cornell and Roberts share net...
Perform the test in Problem 8.134, and report a p-value (two-tailed)? Hematology Insulin-like growth factor 1 (IGF-1) is a hormone that plays an important role in childhood growth and may be...
What test can be used to compare the mean of the two groups? Cancer Age at menarche (onset of menstrual periods) is an important risk factor for breast cancer and possibly ovarian cancer. In general,...
Perform the test in Problem 8.136, and report a two tailed p-value? Cancer Age at menarche (onset of menstrual periods) is an important risk factor for breast cancer and possibly ovarian cancer. In...
How do warehouses and distribution centers differ? What is cross-docking and why might a company choose to cross-dock a product? What kinds of products can be delivered electronically? What kinds...
Strawberry Inc. has historically been an all-equity firm. The analyst expects EBIT to be $1.5B in perpetuity starting one year from now. The cost of equity for the company is 11.5% and the tax rate...
Guzman company received a 60- day, 5 % note for 54,000 dated July 12 from a customer on account. Determine the due date on note. Determine the maturity value of the note and journalize the entry of...

Prove Theorem 5.9(d). d. If W = span(w 1 , . . . , w k ),

Question:

Step by Step Answer:

If v is in W then vw i 0 ...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Mathematics questions