Question: Let H = Span {V 1 , V 2 } and K = Span {V 3 , V 4 }, where Then H and K

Let H = Span {V₁, V₂} and K = Span {V₃, V₄}, where

5 2 - - - - - - - [ - ]

Then H and K are subspaces of R³. In fact, H and K are planes in R³ through the origin, and they intersect in a line through 0. Find a nonzero vector w that generates that line. w can be written as c₁v₁ + c₂v₂ and also as c₃V₃ + C₄V₄. To build w, solve the equation c₁v₁ + c₂v₂ = c₃V₃ + C₄V₄ for the unknown c_j's.

5 2 - - - - - - - [ - ] = [] 3 -12 8 4 5 -28

Step by Step Solution

★★★★★

3.47 Rating (176 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Since the line lies both in H Spanv 1 v 2 and in K Spanv 3 v 4 w can be written both as c 1 v 1 c 2 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Linear Algebra And Its Applications Questions!

An Affirmative Defense of Duress Instructions: Be 58 pages in length (not including the Title page and the References page). Use Times New Roman in 12 pt. font, be double-spaced, and have 1-inch...

Let W V be a subspace. A subspace Z V is called a complementary subspace to W if (i) W Z = {0}, and (ii) W + Z = V, i .e., every v V can be written as v = w + z for w W and z Z. (a) Show that...

Let L1: U v1 and L2: U V2 be linear maps between inner product spaces, with V1, V2 not necessarily the same. Let K1 = L1* L1, K2 = L2* L2. Show that the sum K = K1 + K2 can be written as a...

a) Let u :(2,1,3), v = (-1, 4, 2) and w :(0,], 5) are vectors in R3. i. Express the vector (2, 2, 8) as a linear combination of u, v and w. ii. Find the volume of the parallelepiped determined by the...

Consider a cycle v 1 , v 2 , . . . , v k , v k + 1 in G , where v k + 1 = v 1 , and let ( v i , v i + 1 ) be the edge in the cycle with the largest edge weight. Prove that ( v i , v i + 1 ) does not...

4.1 Exercises 1. Let V be the first quadrant in the xy-plane; that is, let 7. All polynomials of degree at most 3, with integers as coeffi- cients. 8. All polynomials in P,, such that p(0) = 0. a. If...

Let H = Span {u 1 , u 2 , u 3 } andK = Span {v 1 , v 2 , v 3 }, where Find bases for H, K, and H + K. U || V1 = 3 0 -4 3 2 1] U = V = 3 1 1 9 -4 1 U13 = V3 = 2 -3 6 -5 7 6 5

SECTION 15.5 24. f (x, y) = sin(x - y), v= (1,1), P = (5, 6) 45. Use the geostrophi 25. f (x, y ) = tan-1 (xy), v = (1,1), P = (3,4) ern Hemisphere, winds together the isobars, 26. f (x, y ) = exy...

Let H= Span(v, v) and K= Span(vV), where v, V2, Va, and v are given below. 3. V3 -10 4. 3 -6 Then Hand K are subspaces of R. In fact Hand Kare planes in R through the origin, and they intersect in a...

Third Homework Assignment (Due in class, Friday, February 3) Practice Exercises Section 2.5: 6, 8, 10, 12, 14, 15-18 Section 3.1: 2, 10, 14, 16, 22, 23-27 Section 3.2: 2, 5, 12, 17-23 Practice...

A study reported by Griffin et al. compared the rate of pneumonia in 19971999 before pneumonia vaccine (PCV7) was introduced and in 20072009 after pneumonia vaccine was introduced. Read the excerpts...

Accounts Receivable Turnover Hawkeye recorded sales of $240,000 for the year. Accounts receivable amounted to $40,000 at the beginning of the year and $20,000 at the end of the year. Compute the...

ReqA and B Rea C Req D Req E to H Rea 1 Rea J Calculate working capital and the current ratio for each of the past three years. Note: Enter your answers in millions ( i . e . , 5 , 0 0 0 , 0 0 0...

C12. Based on the 2018 GSS, we compare church attendance (ATTEND) between lower- and upper-class respondents. ATTEND is an ordinal measure: 0 = never, 1 = less than once a year, 2 = once a year, 3 =...

Investigate the relationship between total household income (INCOME) and total value of household assets (ASSET). Conduct a statistical analysis to measure how well the two variables correlate....

The survey measured total household assets (ASSET) and total net worth of household (NETWORTH). Use a statistical technique to show that they should have just measured one of the two variables.

A Gallup survey asked a sample of Americans how much confidence they had in the criminal justice system. After recording the responses as well as the race of the respondent, the following table of...

Q1. Easy Use Electronic Center began October with 80 units of inventory that cost $72 each. During October, the store made the following purchases: Oct 3... 10 @ $70 12. 30 @ $65 18 70 @ $57 Easy Use...

The balances below have been extracted from the accounting records of SUMMER LTD at 31 December 2016 DR. "000E 90 CR 000E 95 13 115 86 5 1005 730 176 Land Equipment at cost Equipment depreciation at...

A bank has two types of branches. A satellite branch employs 3 people, requires $400,000 to construct and open, and generates an average daily revenue of $10,000. A full-service branch employs 6...