13. Which of the following sets of vectors DOES NOT span R*?{{)() (}{()0{O ()0}{()) (}(a)3.(b)(c)(d)(e) None of the above - they all span R3(3 1 1 20 0 -20 0 -1 114. Let A =The mumber of free variables in the linear system Ar = 0 is(a) 0(b) 1(c) 2(d) 3(e) None of the above{() (O} -md B - {() ()} «15. Consider the two bases B =of R2. What is the transition matrix from B,to B2?(b)6 )(G )(c)(d)(e) None of the above

Answered: Image /qna-images/answer/40a843e7-5ab6-41b1-a6c4-05c2817c8338.jpg

Answered: 13. Which of the following sets of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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Similar questions

Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Suppose masses m1, m2, m3, m4 are located at positions x1, x2, x3, x4 in a line and connected by springs with constants k12, k23, k34 whose natural lengths of extension are l12, l23, l34. Let f1, f2, f3, f4 denote the rightward forces on the masses, e.g., f1 = k12(x2 - x1 - l12). (a) Write the 4 x 4 matrix equation relating the column vectors f and x. Let K denote the matrix in this equation. (b) What are the dimensions of the entries of K in the physics sense (e.g., mass times tim, distance divided by mass, etc.)? (c) What are the dimensions of det(K), again in the physics sense? (d) Suppose K is given numerical values based on the unit meters, kilograms, and seconds. Now the system is rewritten with a matrix K' based on centimeters, grams, and seconds. What is the relationship of K' to K? What is the relationship of det(K') to det(K)?
17.Consider the linear system dxdt=a11x+a12y,dydt=a21x+a22y,dxdt=a11x+a12y,dydt=a21x+a22y, where a11, a12, a21, and a22 are real-valued constants. Let p = a11 + a22, q = a11a22 − a12a21, and Δ = p2 − 4q. Observe that p and q are the trace and determinant, respectively, of the coefficient matrix of the given system. Show that the critical point (0, 0) is a a.Node if q > 0 and Δ ≥ 0; b.Saddle point if q < 0; c.Spiral point if p ≠ 0 and Δ < 0; d.Center if p = 0 and q > 0. Hint: These conclusions can be reached by studying the eigenvalues r1 and r2. It may also be helpful to establish, and then to use, the relations r1r2 = q and r1 + r2 = p.

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