1. 2. 3. 4. 5. Let u (2, 3, -4) and v - = (2,5, -1)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. 2. 3. 4. 5. Let u (2, 3, -4) and v - = (2,5, -1) be two vectors of size 3. (a) Determine the cosine of the angle between u and v. (b) Find the unit vector w₁ in the direction of u. (c) Find the unit vector w₂ in the direction of v. Let u, V. and w be three vectors in R³. Suppose that u and v are orthogonal to w. Using the properties of inner product: (a) Show that u + v is orthogonal to w. (b) Show that for any scalar a, au is also orthogonal to w. Let W be the line with equation y = 3 - 2x. Is W a subspace of R2? Justify your answer. Let W = a a + c C : a, b, c ER be a subset of R4. (a) Show that W is a subspace of R4. (b) Find a set S of 4-vectors that spans W. Let P be the plane in R³, with equation 2xy +z = 0. (a) Show that P is a subspace of R³. (b) Find a set S of 3-vectors that spans W. Hints: For question 3 (similar to question 5), any vector in W is of the form (x, y) where y = 32x, i.c., any vector in W is of the form (x, 3 — 2x). - 1. 2. 3. 4. 5. Let u (2, 3, -4) and v - = (2,5, -1) be two vectors of size 3. (a) Determine the cosine of the angle between u and v. (b) Find the unit vector w₁ in the direction of u. (c) Find the unit vector w₂ in the direction of v. Let u, V. and w be three vectors in R³. Suppose that u and v are orthogonal to w. Using the properties of inner product: (a) Show that u + v is orthogonal to w. (b) Show that for any scalar a, au is also orthogonal to w. Let W be the line with equation y = 3 - 2x. Is W a subspace of R2? Justify your answer. Let W = a a + c C : a, b, c ER be a subset of R4. (a) Show that W is a subspace of R4. (b) Find a set S of 4-vectors that spans W. Let P be the plane in R³, with equation 2xy +z = 0. (a) Show that P is a subspace of R³. (b) Find a set S of 3-vectors that spans W. Hints: For question 3 (similar to question 5), any vector in W is of the form (x, y) where y = 32x, i.c., any vector in W is of the form (x, 3 — 2x). -
Expert Answer:
Related Book For
General Chemistry Principles And Modern Applications
ISBN: 9780132931281
11th Edition
Authors: Ralph Petrucci, Jeffry Madura, F. Herring, Carey Bissonnette
Posted Date:
Students also viewed these databases questions
-
1. For each of the variables listed in the table below, indicate: the type of variable - quantitative discrete, quantitative continuous or qualitative, and the level of measurement for the variable -...
-
Q2. (a) The costs per unit for Starlight Sdn Bhd are as following: Direct material Direct labour Manufacturing Overhead: Variable Fixed Other Fixed Costs: Selling and distribution Administrative...
-
Which of the following transactions does not take place in a market for a factor of production? a. Karl provides plumbing services for a plumbing company and receives an hourly wage from the company...
-
E-max sold Dishwashers on credit, worth OMR 55,000 to customers, out of these Dishwashers customers return damaged Dishwashers for OMR 6,000. Record the entry for the Dishwashers returned? a. Debit...
-
An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives...
-
Cream of tartar, a common ingredient in cooking, is the common name for potassium bitartrate (abbreviated KBT, molar mass = 188.2 g/mol). Historically, KBT was a crystalline solid that formed on the...
-
On January 7, Red Tucker, Inc., paid $254,700 for equipment used in manufacturing automotive supplies. In addition to the basic purchase price, the company paid $500 transportation charges, $300...
-
Select a company you are interested in and obtain its annual reports by going to the companys website. Download the annual report for the most recent year. (On many companies websites, you will need...
-
JT produces laser printers for the global market in its Weihai facility that are shipped to regional distribution centres afterwards before being sold to retailers. In the past month, the demand for...
-
Fultz and Hunter form a partnership on January 1, 2018, contributing $59,000 and $20,000, respectively. The partnership had net income of $164,000. Based on the partnership agreement, Fultz's share...
-
ken: Borrow money to buy spot. Simultaneously sell the futures. While carrying the spot asset, some income might be received. At maturity of the futures contract, use the spot to deliver on the...
-
What security provides a good estimate of the short-term nominal risk-free rate?
-
A person who makes a will. a. benefi ciary b. bequest c. codicil d. decedent e. devise f. executor g. holographic will h. inter vivos i. intestate j. personal representative k. residuary l. settlor...
-
The person named in a will to administer the estate. a. benefi ciary b. bequest c. codicil d. decedent e. devise f. executor g. holographic will h. inter vivos i. intestate j. personal representative...
-
Differentiate between interest rate risk and reinvestment rate risk.
-
How does a firm formally declare bankruptcy?
-
Find the magnitude E of the electric field at a distance from the axis of the cylinder for r < ro. Remember that we've chosen the label / to represent the length of the cylindrical Gaussian surface....
-
QUESTION 9 HC-O-C-R R-C-O-CH HC-O-P-O-CH-CH-NH3* O || O a. Phosphatidic acid, Serine O b. Lysophosphatidic acid, Serine, Free FA O c. Lysophosphatidylserine, Free FA O d. 2 Free FAs, Serine, Glycerol...
-
Draw plausible structures corresponding to each of the following names. (a) Pentamminenitrito-N-cobalt(III) ion; (b) Ethylenediaminedithiocyanato-S-copper(II); (c) Hexaaquanickel(II) ion.
-
In the reaction A products, at t = 0, [A] = 0.1565 M. After 1.00 min, [A] = 0.1498 M, and after 2.00 min, [A] = 0.1433 M. (a) Calculate the average rate of the reaction during the first minute and...
-
Write chemical equations to represent the following reactions. (a) Calcium phosphate is heated with silicon dioxide and carbon, producing calcium silicate (CaSiO 3 ), phosphorus (P 4 ), and carbon...
-
List the modifications of the standard audit report that normally do not result in a qualification, a disclaimer, or an adverse opinion.
-
When more than one auditor is involved in an audit of a company's financial statements, what two decisions about reporting must the principal auditor make?
-
What disclosure is made in the principal auditors' report if they decide to assume responsibility for other auditors' work? If they decide not to assume responsibility for other auditors' work?
Study smarter with the SolutionInn App