Choose your favorite unique vector b in R3 with no 0 entries. What is your vector...

Choose your favorite unique vector b in R³ with no 0 entries.

What is your vector b?
Based on the “Equivalent Conditions for a Non-Singular Matrix” on page 123 in our text, why must Ax = b have a unique solution in this situation?

Solve the equation Ax = b the following three ways (you should get the same answer each way!) Recall – calculator OK, in fact suggested. (24 points – 8 points each)
- Solve the equation Ax = b using Gaussian Elimination. Show the augmented matrix and then use “ref” or “rref” on your calculator. Complete with back substitution.
- Solve the equation Ax = b using the inverse of (A), which you have already calculated above.
- Solve the equation Ax = b using Cramer’s Rule. Identify A, A_x, A_y, A_z and their determinants.
Express b as a linear combination of the column vectors of A.

12. In practice involving very large systems with square matrices of coefficients, Gaussian Elimination is often implemented by using LU factorization. Why do you think that is the case? 10-20 words (more if you want).

Replace the first row of your matrix A with the second row of your matrix A. Call this new 3x3 matrix with 2 equal rows B.

13. What is your matrix B?

14. Calculate the determinant of B without a calculator. Perform at least one row or column operation on the Determinant as part of your calculation procedure.

15. Solve the Matrix equation Bx =0

What is the general solution for x in terms of (say) any real number t?
Determine a specific non-zero solution for x (I.e. assign t to a specific real number)?
Verify that Bx = 0 for your specific solution for x.

Expert Solution

Colby Messinger answered 2 years ago

Below is a proof of Theorem 4.1.1 (b): For the zero vector ⃗0 in any vector...

Below is a proof of Theorem 4.1.1 (b): For the zero vector ⃗0 in any vector space V and k ∈ R, k⃗0 = ⃗0. Justify for each of the eight steps why it is true. k⃗0+k⃗0=k(⃗0+⃗0) = k ⃗0 k⃗0 is in V and therefore −(k⃗0) is in V . It follows that (k⃗0 + k⃗0) + (−k⃗0) = (k⃗0) + (−k⃗0) and thus k⃗0 + (k⃗0 + (−k⃗0)) = (k⃗0) + (−k⃗0). We conclude that k⃗0 + ⃗0...

Choose one of your favorite brands. In your initial discussion post, explain what about the brand...

Choose one of your favorite brands. In your initial discussion post, explain what about the brand makes it compelling to you. How does the company use marketing to communicate the brand? Identify at least one way that the company could improve its brand communications. What should the company consider to avoid unethical marketing? How could unethical marketing affect its brand?

A non-uniform b-spline curve knot vector is given as (-1, -1, -1, -1/2, 0, 0, 0,...

A non-uniform b-spline curve knot vector is given as (-1, -1, -1, -1/2, 0, 0, 0, 1, 1, 1, 3/2, 2, 2, 3, 3, 3, 3). Show the equation diagrammatically and sketch the curve with their respective control polygons if the curve is cubic (degree 3, order 4).

choose two of your favorite brand and devise an idea for an Alexa "skill"that consumers could...

choose two of your favorite brand and devise an idea for an Alexa "skill"that consumers could find useful. How will these skill help sell more of the brands" produts and/or increase customer loyalty.

Let a and b be non-parallel vectors (algebraically a1b2 −a2b1 /= 0). For a vector c...

Let a and b be non-parallel vectors (algebraically a1b2 −a2b1 /= 0). For a vector c there are unique λ, µ real numbers such that c = λ· a+µ·b. proof?

Choose two of your favorite foods that contain over 100mg of sodium. List them with the sodium intake

several meal planning tools are available for a diabetic client to use. If you were diagnosed with diabetes, which food plan would work best for your lifestyle? Research the various diet and meal plans and defend your answer. Include one to two references with sources cited throughout posting and reference in reference list.2. Choose two of your favorite foods that contain over 100mg of sodium. List them with the sodium intake (cite your references and include in a reference list...

Choose your favorite publicly-traded company other than Facebook that we did in class. Then, do the...

Choose your favorite publicly-traded company other than Facebook that we did in class. Then, do the following: 1) Calculate its beta using three-year historical prices 2) Calculate its re (cost of equity) 3) Calculate its rd (cost of debt) 4) Find out how much debt is has (see balance sheet and the notes that accompany it) 5) Calculate its market capitalization 6) Using the above information, calculate its WACC Please show all of your computations and submit the Excel file.

Think of your favorite retail stores. What do they do that encourages your loyalty? what do...

Think of your favorite retail stores. What do they do that encourages your loyalty? what do you like about the in-store experience? what further improvements could they make?

What is the arithmetic mean for the following stock returns: R1=6.3%, R2=4%, R3=7.2%? A) 17.5% B)...

What is the arithmetic mean for the following stock returns: R1=6.3%, R2=4%, R3=7.2%? A) 17.5% B) 4.375% C) 5.833% D) 5.825% E) 18.512%

1. What is your favorite classic game system and why? What aspects of the hardware and...

1. What is your favorite classic game system and why? What aspects of the hardware and software interface elements in the game system that appeal to you? What are some of your favorite games that you enjoy playing and why? 2. How have interfaces evolved over the course of video game history? Think of a game you play and list and discuss the key features in the game's interface. 3. How can a game interface address accessibility issues? Choose a...

Question