Question: Write the following positive definite quadratic forms as a sum of pure squares, as in (3.71): (a) 16x21 + 25x22 (b) 5x21 - 2x1x2 +

Write the following positive definite quadratic forms as a sum of pure squares, as in (3.71):
(a) 16x21 + 25x22
(b) 5x21 - 2x1x2 + 4x22
(c) 5x21 + 4x1x2 + 3x22
(d) 3x21 -2x1x2 - 2x1x3 + 2x22 + 6x23
(e) x21 + x1x2 + x2 x3 + x23
(0) 4x21 - 2x1x2 - 4x1x3 + 1/2 x22 - x2x3 + 6x23
(g) 3x21 + 2x1x2 + 3x22 + 2x2x3 + 3x23 + 2x3x4 + 3x24

Step by Step Solution

★★★★★

3.51 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a z 2 1 z2 2 where z 1 ... 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

Document Format (1 attachment)

952-M-L-A-E (2063).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Show that Q(0) . 0 for every quadratic form Q. Since every quadratic form passes through the origin (exercise 3.93), a positive definite quadratic form has a unique minimum (at 0). Similarly a...

Write down and solve an optimization principle characterizing the largest and smallest eigenvalue of the following positive definite matrices: 4 1 111 214 13 461 141 641 412 21

Write the following quadratic forms on M2 as a sum of squares. Which are positive definite? (a) x2 8xy + y2 (b) x2 - 4xy + 7y2 (c) x2 - 2x y - y2 (d) x2 + 6x y

I want these code to converted in PYTHON. it just a conversion don't make an excuse 1 question policy if u don't want to answer please leave my question will refunded. Question 24: Write a C++...

I want these code to converted in PYTHON. it just a conversion don't make an excuse 1 question policy if u don't want to answer please leave my question will refunded. Question 30: Write a C++...

I want these code to converted in PYTHON. it just a conversion don't make an excuse 1 question policy if u don't want to answer please leave my question will refunded. and also the remarks section....

Construct an orthonormal basis for R3 with respect to the inner products defined by the following positive definite matrices: (a) (b) 2 23] 420 142 311

Please provide compelte solution, show full calculations, explanations and proofs to the following question: Please only answer question 2 only 2. Portfolio optimization with only risky assets:...

Please provide complete solution, show full calculations, explanations and proofs to the following question: Please answer question 4 4. The Capital Asset Pricing Model (CAPM): The CAPN may be the...

Problem 1: a) A matrix A has the following spectrum d1 = 0, 12 = 51 13 = 2, da = 7. Is the matrix positive definite? Is it singular? Explain why or why not in each case. b) If the eigenvalues and...

Suppose the Alpha Manufacturing Corporation is experiencing extreme financial difficulties and is considering bankruptcy. Its shareholders are currently almost equally divided about whether or not...

Reconsider the water quality data in Exercise 6-24. Construct a box plot of the concentrations and write an interpretation of the plot. How does the box plot compare in interpretive value to the...

Suppose that in a state lottery game players choose three digits, each from the set 0 to 9, as they do in many state lottery games. But for this game, what counts is the sum of the three chosen...

Who was the offeror? Does the UCC apply in this case?

Find A-1 using Theorem 2.1.2. a. b. 503 514 212 3 310

Let (a) Evaluate A-1 using Theorem 2.1.2. (b) Evaluate A-1 using the method of Example 4 in Section 1.5. (c) Which method involves less computation? 1292 1282 3533 1211

7x1 - 2x2 = 3 3x1 + x2 = 5 Solve by Cramer's rule, where it applies.

For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger...

Professor Wendy Smith has been offered the following opportunity: A law firm would like to retain her for an upfront payment of $50,000. In return, for the next year the firm would have access to...

Answer all questions with explanation The Appliance Parts Company manufactures small motors used in various household appliancees. Extensive reliability testing has determined that the failure...