Consider the quadratic form f(x) = x + x3 + x3 + 4x1X2 + 4x2x3 +...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the quadratic form f(x) = x + x3 + x3 + 4x1X2 + 4x2x3 + 4x3x1. (a) Find the real symmetric matrix A so that f(x) = x' Ax. (b) Find an orthogonal matrix Q so that the change of variables x = Qy transforms the quadratic for f(x) into one with no cross-product terms, that is, diagonalize the quadratic form f(x). Give the transformed quadratic form. (c) Find a vector x of length 1 at which f(x) is maximized. (d) Is the form f(x) positive definite? Explain your answer. (e) Describe the set of points (x1, X2, X3) E R satisfying the equation x + x3 + x3 + 4x1x2 + 4x2x3 + 4x3X1 = 0. That is, name the shape in standard position and find the vector about which it is centrally symmetric. You may also find the vector about which it has been rotated as in the slides. Consider the quadratic form f(x) = x + x3 + x3 + 4x1X2 + 4x2x3 + 4x3x1. (a) Find the real symmetric matrix A so that f(x) = x' Ax. (b) Find an orthogonal matrix Q so that the change of variables x = Qy transforms the quadratic for f(x) into one with no cross-product terms, that is, diagonalize the quadratic form f(x). Give the transformed quadratic form. (c) Find a vector x of length 1 at which f(x) is maximized. (d) Is the form f(x) positive definite? Explain your answer. (e) Describe the set of points (x1, X2, X3) E R satisfying the equation x + x3 + x3 + 4x1x2 + 4x2x3 + 4x3X1 = 0. That is, name the shape in standard position and find the vector about which it is centrally symmetric. You may also find the vector about which it has been rotated as in the slides.
Expert Answer:
Related Book For
Fundamentals of Physics
ISBN: 978-0471758013
8th Extended edition
Authors: Jearl Walker, Halliday Resnick
Posted Date:
Students also viewed these mathematics questions
-
In each case, find a symmetric matrix A such that q = XTBX takes the form q = XTAX. (a) (b) (c) (d) 2 101 011 103 212 145
-
In each case, find a symmetric matrix A such that (v, w) = vTAw. (a) (b) (c) (d) +5vzw = vy 2 + 2vy w, + 2vyw
-
In Figure, a block slides down an incline. As it moves from point A to point-B, which are 5.0 m apart, force F acts on the block, with magnitude 2.0 N and directed down the incline. The magnitude of...
-
Four wooden beams, each of length 2a, are nailed together at their midpoints to form the support system shown. Assuming that only vertical forces are exerted at the connections, determine the...
-
Find (a) The density (y) of y, (b) The conditional density fX|Y(x | y) of X given Y. Let fX,Y(x,y) be constant on the region shown in Figure. 4. 3. 3 4 2.
-
You are discussing your retirement plan with Dan Ervin when he mentions that Sarah Brown, a representative from Skandla Financial Services, is visiting West Coast Yachts today. You decide that you...
-
Distinguish briefly between the three types of corporate fraud.
-
David Rodriguez owns a chain of travel goods stores, Rodriguez Travel Goods. Last year, his sales staff sold 25,000 suitcases at an average sales price of $150. Variable expenses were 60% of sales...
-
Choose one of the four basic leader behavior styles suggested by Hersey and Blanchard. Discuss the specifics of the task and relationship behaviors of the chosen style. Provide a realistic example of...
-
You are the contracting officer for a CPFF service contract for routine and emergency maintenance of testing equipment in the amount of $1,200,000. The contractor is not required to provide any...
-
Professor Stocks purchased her house in 2003 for $310,000 and can sell it in today's market for $800,000 (yes!). What is the ACB and FMV?
-
C&A Museum has 1,500,000 visitors per year. Each visitor spends an average of 2 hours in the museum. What is the average number of visitors in the museum on a given day if the museum is open 300 days...
-
3- Temperature distribution on the plate is modelled by the Laplace equation VT = 0. Boundary condition can be seen in the figure. Discretize the Laplace Equ. By using centered finite difference...
-
The following information concerns production in the Baking Department for August. All direct materials are placed in process at the beginning of production. ACCOUNT Work in Process-Baking Department...
-
FIFO and LIFO Costs Under Perpetual Inventory System The following units of an item were available for sale during the year: Beginning inventory 23 units at $42 Sale 16 units at $63 First purchase 23...
-
Sam urgently needs $30000. He goes to a local finance company who agrees to lend this amount and proposes two payment options. A) Pay $36,000 at the end of the year. B) Pay $3,000 every month for a...
-
Tech Solutions is a consulting firm that uses a job-order costing system. Its direct materials consist of hardware and software that it purchases and Installs on behalf of its clients. The firm's...
-
The power company must generate 100 kW in order to supply an industrial load with 94 kW through a transmission line with 0.09 resistance. If the load power factor is 0.83 lagging, find the...
-
How much work must be done by a Carnot refrigerator to transfer 1.0 J as heat? (a) From a reservoir at7.0 o C to one at 27 o C, (b) From a reservoir at -73 o C to one at27 o C, (c) From a reservoir...
-
In a long jump, an athlete leaves the ground with an initial angular momentum that tends to rotate her body forward, threatening to ruin her landing. To counter this tendency, she rotates her...
-
Two charged concentric spherical shells have radii 10.0 cm and 15.0 cm. The charge on the inner shell is 4.00 x 10-8 C, and that on the outer shell is 2.00 x 10-8 g. Find the electric field (a) At r...
-
Make a bar chart of \(\mathrm{CO}_{2}\) footprint divided by embodied energy, using data from the data sheets of Appendix A, Table A10, for a. Cement b. Low carbon steel c. Copper d....
-
a. A range of office furniture includes a chunky hardwood table weighing \(18 \mathrm{~kg}\) and a much lighter table with a \(3.0 \mathrm{~kg}\) virgin aluminium frame and a \(3.0 \mathrm{~kg}\)...
-
a. Window frames are made from extruded aluminium. It is argued that making them instead from extruded PVC would give a product with a lower embodied energy and carbon footprint. If the section shape...
Study smarter with the SolutionInn App