solve the given problems 13. Let A = 1 0 3 1 2 1 1 2 (a)
Fantastic news! We've Found the answer you've been seeking!
Question:
solve the given problems
Transcribed Image Text:
13. Let A = 1 0 3 1 2 1 1 2 (a) Taking X = = (1, 1, 2) shows that (1,0,4)= AX is in the range of A. Show that (1,0, 4) is a linear combination of (1,3,1), (0, 1, 1), and (1,2,2). (b) The vector v = = 2(1,3,1) + (0, 1, 1)3(1,2,2) = (1,1,5) is a linear combi nation of the columns of A. Find X so that AX = v. (c) Is the vector (3,7,5) in the subspace spanned by (1,3,1), (0, 1, 1), and (1,2,2)? (d) Show that (1, 2, 2) is a linear combination of (1,3,1) and (0,1,1). (e) Show that R(A) is the subspace spanned by (1,3,1) and (0, 1, 1). 14. Let E= 2 0 1 1 1 1 1 3 0 1 1 2 1 2 2 3 2 1 1 2 (a) Find vectors that span N(E) the nullspace of E. (b) Find vectors that span R(E) the range of E. (c) Find vectors that span N(E) the nullspace of E'. (d) Find vectors that span R(E') the range of E'. 13. Let A = 1 0 3 1 2 1 1 2 (a) Taking X = = (1, 1, 2) shows that (1,0,4)= AX is in the range of A. Show that (1,0, 4) is a linear combination of (1,3,1), (0, 1, 1), and (1,2,2). (b) The vector v = = 2(1,3,1) + (0, 1, 1)3(1,2,2) = (1,1,5) is a linear combi nation of the columns of A. Find X so that AX = v. (c) Is the vector (3,7,5) in the subspace spanned by (1,3,1), (0, 1, 1), and (1,2,2)? (d) Show that (1, 2, 2) is a linear combination of (1,3,1) and (0,1,1). (e) Show that R(A) is the subspace spanned by (1,3,1) and (0, 1, 1). 14. Let E= 2 0 1 1 1 1 1 3 0 1 1 2 1 2 2 3 2 1 1 2 (a) Find vectors that span N(E) the nullspace of E. (b) Find vectors that span R(E) the range of E. (c) Find vectors that span N(E) the nullspace of E'. (d) Find vectors that span R(E') the range of E'.
Expert Answer:
Answer rating: 100% (QA)
The image you provided contains several problems relating to linear algebra concepts such as vector spaces range column space and nullspace of a matri... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions

solve the given problems Let f(x) = ln(1 + x). i. Calculate the first, second, third, and fourth derivatives of f. ii. Using these derivatives, obtain the Taylor polynomials of degree n of f at b =...

Solve the initialvalue problems given in Problems 35 and 36. (a) (b) 3 011 , =10311 Lo 2I 9 i(0)=1 2 13

B. Use MATLAB SYNTAX solve the given problems below. Write the MATLAB syntax you use and the MATLAB output in the space provided. 1. Use Cramer's Rule to show the solution of W BE 0 (0,0,0) 248x...

Slip Systems had no shortterm investments prior to 2015. It had the following transactions involving shortterm investments in availableforsale securities during 2015. Feb. 6 Purchased 3,400...

What purpose do audits and generally accepted accounting principles (GAAPs) serve in todays business world?

How has history defined and shaped modern ethics in nursing research? What are some additional issues or personal examples you can think of that can further our understanding of ethics in research?...

The chapter provides sample goals for an initial sales call on a prospect. (a) What other goals can you come up with that might be appropriate for an initial sales call? (b) Develop three or four...

If you were in Alexs position, 1. What type of coaching style would you choose when working with James? 2. What behaviors would you engage in while coaching James in order to ensure that he is...

1. Graph the functions: a. y = 2x (= b. y =

Joe and Jessie are married and have one dependent child, Lizzie. Lizzie is currently in college at State University. Joe works as a design engineer for a manufacturing firm while Jessie runs a craft...

Imagine you work for a tech company, and its employees want to avoid the long commute by working from home. The company's CEO has agreed to allow this shift. Write her an email explaining the plans....

(a1, a2,..., Consider the following recursive algorithm, which takes as input a sequence , an) of n numbers, where n is a power of two, i.e., n = 2k for some integer k > 0: Algorithm MYSTERY (a1,...

JenCo reported the following information in its financial statements for three successive quarters during the 2021 fiscal year ($ in millions): Balance sheets: Three Months Ended 2021/05/01 (Q3)...

Albert House, current workers' compensation carrier has provided Albert House, with a forecasted amount for 2024's workers' compensation claims. The total projected losses for 2024 are almost twice...

Based on historical data, the Hospital of St. Jacques wants to have 7 bags of B positive blood to every 2 bags of B Negative, furthermore, they want to have 3 bags of B negative blood for every 1 bag...

You want to be able to withdraw $25,000 each year for 15 years. Your account earns 7% interest. How much do you need in your account at the beginning?

Risk free rate 2% market risk premium 9% tax rate 3%: cost of debt 8%: Debt to equity ratio 1.5 What is the WACC. a) if the company has a beta of 1.2? And b) if the company has a beta of 0.9?

Find the radius of convergence in two ways: (a) Directly by the CauchyHadamard formula in Sec. 15.2. (b) From a series of simpler terms by using Theorem 3 or Theorem 4.

Refer to Table 8.8. Conduct a residual analysis with the model of no threefactor interaction to describe the nature of the interaction. Table 8.8: Loglinear Models for Injury, SeatBelt Use, Gender,...

For noncanonical links in a GLM, show that the observed information matrix may depend on the data and hence differs from the expected information. Illustrate using the probit model.

Fit the RC model to Table 9.3. Interpret the estimated scores. Does it fit better than the uniform association model? Table 9.3: Opinions about Premarital Sex and Availability of Teenage Birth...

We normally think that dissipative forces tend to decrease the velocity of an object. This is correct for isolated systems. Consider the case of an artificial satellite of mass \(m\) in a circular...

Determine the work required to transport \(10 \mathrm{~kg}\) of material from Earth to the ISS, the International Space Station, in orbit \(420 \mathrm{~km}\) above the Earth's surface.

An artificial satellite of mass \(m=3.4\) ton is in a circular orbit at the altitude \(h_{1}=5000 \mathrm{~km}\). Due to various causes, it gradually loses energy and reaches an altitude \(h_{2}=600...
Study smarter with the SolutionInn App