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2. (10 pts.) Describe the set of all b for which the system bi 1 201...
Let A = and b = . Show that the equation Ax = b does not have a solution for some choices of b, and describe the set of all b for which Ax = b does have a solution. How can it be shown that the equation Ax = b does not have a solution for some choices of b? A. Row reduce the augmented matrix [A b] to demonstrate that [A b] has a pivot position in every row B. Find a vector...
4. (35 pts) Consider the system defined by: xit 5x1-2x2-R (1) #2-2x, +2x2 F) a) Compute the natural frequencies and the mode shapes. /dland -JS -2N5 b) Calculate the response for F(t)-F(t)-0 and initial conditions xo- e) Calculate the response for F-cosr, F,(o)-0 and initial conditions and -0. 0 d) Calculate Bi and B2 such that the system: -2x1 + 2x2-B2cos/6t does not experience resonance. 4. (35 pts) Consider the system defined by: xit 5x1-2x2-R (1) #2-2x, +2x2 F) a)...
question B2 B. Short Essay (write 2): 6-8 sentences / 10 pts. each (20 pts.) Bi. Summarize the four main themes of Complexity in the field of Eco-geomorphology B2. Describe the role of Magnitude and Frequency in relation to Geomorphic Work/Processes - How does Geomorphic Effectiveness fit into the discussion? B3. Explain the issues with Cross-Scale Relationships
L 0 0 bi b3 (a) (5 pts) Solve the system of equations Ax- b for x. (b) (5 pts) Write your solution in the form of x A- b.
be the set of all points a + bi, where a, b E Q and which lie inside the shaded square shown (a) Is bounded? (b) What are the limit points of , if any? |(c) Is closed? (d) What are its interior and boundary points? (e) Is open? (f) Is connected? (g) Is a region? (h) What is the closure of 0? (i) Is compact? (i) Is the closure of 2 compact? 8. Let
b. - 2 -1 1 and b Let A = Show that the equation Ax =b does not have a solution for all possible b, and -3 0 3 4-2 2 b3 describe the set of all b for which Ax b does have a solution How can it be shown that the equation Ax = b does not have a solution for all possible b? Choose the correct answer below. O A. Find a vector b for which the...
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations) Question (7) Consider...
4 Given Ax = b 2 4 6 4 bi 4 A=12576 23 5 2 b3 1. Reduce [A b]to [U cl,so that Aa b becomes a triangular system Ux-c. 2. Find the condition on b1, b2, bs for Aabto have a solution. 3. Describe the column space of A. Which plane in R3? 4. Describe the nullspace of A. Which special solutions in R4? 5. Reduce [U c]to[R d]: Special solutions from R, particular solution from d. 6. Find...
need help on number 13 Exercises 11-16. Represent each linear system in marrix form. Solve by Gauss elimination when the system is consistent and cross-check by substituting your solution set back into all equations. Interpret the solution geometrically in terms planes in R3. of 2x1 +3x2 x3 = 1 4x1 7x2+ 3 3 11. 7x1 +10x2 4x3 = 4 3x1 +3x2+x3 =-4.5 12. x1+ x2+x3 = 0.5 2x-2x2 5.0 x+2x2 3x3 1 3x1+6x2 + x3 = 13 13. 4x1 +8x2...
need answers for all 1. Which terminology correctly defines the system property described below? (2 pts) A system is stationary and does not vary over time. (a) Linearity (b) Time invariance (c) Periodicity (d) Causality 2. Which terminology correctly defines the system property described below? (2 pts) (a) Linearity (b) Time invariance (c) Periodicity (d) Causality 3. Which is true about a linear and time-invariant (LTI) system? (2 pts) (a) The system's output is always equivalent to an impulse reponse....