Note that and u, are orthogonal it can be shown that t h e wspawned by...
Note that u, and u are orthogonal. It can be shown that ug is not in the subspace W spanned by u, and up. Use this to construct a nonzero vector v in R that is orthogonal tou, and un The nonzero vector v= | is orthogonal to u, and up.
#11 6.3.19 A Question Help 0 Let uy = 2 -2, and uz = 0 . Note that u, and uz are orthogonal but that uz is not orthogonal to u, oruz. It can be shown that uz is not in the subspace 2 W spanned by U, and up. Use this fact to construct a nonzero vector v in R3 that is orthogonal tou, and uz. A nonzero vector in R3 that is orthogonal tou, and uz is v=
only a-i T or F lit khd where it came from 4. You do not need to simplify results, unless otherwise stated. 1. (20pts.) Indicate whether each of the following questions is True or False by writing the words "True" or "False" No explanation is needed. (a) If S is a set of linearly independent vectors in R" then the set S is an orthogonal set (b) If the vector x is orthogonal to every vector in a subspace W...
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=
Y(z) c(t), C(s) r(t), R(S) + - et), E(S) E*(s), Ez To- D(z) G (s) = (1-e-STºys H(s) 32. If the system above has Y(z)R(z)= 1+z), and if the input is the unit step r(t)=u(t), then the signal y[n]= u[n]-e-Tou[n-1) | u[n]+u[n-1] a) c) u[n] + u[n-1) d) none above 33. If the system above has Y(z)/R(z)= 1+z), the dc gain of the system is C(z)/R(z)= b) 1/2 c)2 d) none above a) o 34. If the system above has...
how can show two eqntions that is, by H/W aIng(E) Recalling that H/W s-king and (T)E=U-T the foregoing condition implies that E-U that is, by H/W aIng(E) Recalling that H/W s-king and (T)E=U-T the foregoing condition implies that E-U that is, by H/W aIng(E) Recalling that H/W s-king and (T)E=U-T the foregoing condition implies that E-U that is, by H/W aIng(E) Recalling that H/W s-king and (T)E=U-T the foregoing condition implies that E-U
3. Given pairwise orthogonal vectors u, v, w ER(each vector is orthogonal to every other), with || || = ||0|| = ||w|| = 1, and C1, C2, C3 € R, prove that || Cu + c2v + c3w||2 = cſ + cx+cz.
#12 6.3.20 s Question Help 5 0 Let un 2. u2 -8 and uz = 1 Note that u, and uz are orthogonal. It can be shown that ug is not in the subspace W spanned by u, and up. Use this to - 1 0 construct a nonzero vector v in R3 that is orthogonal to u, and up. 4 The nonzero vector v = is orthogonal to u, and u2
full proofs for both and please write legibly 5. Let T be an orthogonal transformation on a finite dimensional vector space V over the real numbers, with an inner product. Show that D(T) = $1. 6. Show that if u,...,U, are orthonormal vectors in R, (see (15.7)), then D(uj, ..., Un) = 1.
DETAILS LARLINALG8 5.R.022. Determine all vectors that are orthogonal to u. (If the system has an infinite number of solutions, express V, V, and v, in terms of the parameters s and t.) u = (1, -2, 1) V-