By Howard Anton, Robert C. Busby
From one of many optimum authors in better schooling comes a brand new linear algebra textbook that fosters mathematical pondering, problem-solving skills, and publicity to real-world purposes. with out sacrificing mathematical precision, Anton and Busby concentrate on the features of linear algebra which are probably to have useful price to the scholar whereas now not compromising the intrinsic mathematical kind of the topic. all through modern Linear Algebra, scholars are inspired to examine principles and difficulties from a number of issues of view.
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Additional resources for Contemporary Linear Algebra, Student Solutions Manual
Ion and addition: k(a, 0, 0) = (ka, 0, O) and (a1. a, 0) + (az, 0, 0) = (a1 + az, 0, 0). (b) This seL of ''cctors is not a subspace; it is not closed under scalar multipllcation. · subspace. lf b = a+ c, then . kb = ka + kc. If b1 ;;;·a 1 + c1, and b2 = nz + cz, then (b1 + bz) = (aJ + a2) + (c1 + cz) . (d) This set of vectors is not a subspace; it is not closed under addition or scalar multiplication. 23. (a) . 24. Sets (a) and (b) are not subspaces. Sets (c) and (d) are suhspaces. 25. re v (l,O , 1, 0) .
94v) = (a) No. 1t is not closed under either addition or scalar multiplication. (b) 34. 59m + 0. 27). ) is weighted twice as heavily as Test 1 and Test 2. DISCUSSION ANP DISCOVERY 89 i 35. (a) kt = kz = k3 = k4 = ~ (b) k1 = k2 = k3 = k4 = k& = (c) The comp onents of x; = ~r 1 + ! r 2 + ~ r:; represent the average total population of Philadelphia, Bucks, and Delaware counties in each of the sampled years. n 36. v = L vk k= l =DISCUSSION AND DISCOVERY Dl . re do not lie on a line. (b) T hree nonzero vectors .
Then, for any scalar k , we have kz = k(x + y) = kx + ky, where kx is in W1 and ky is in W:~ (since w, and w2 are subspaces); thus kz IS in w} + w2. Finally we show that WI + w2 is closed under addition: Suppose Z l =X) + Yl and Z 2 = X 2 + Y2 o where X) and X2 are in W1 and Y• and Y2 are in W2 . Then z 1 + Z2 == (x1 + y, ) + (x2 + Yz) = (x1 + x2) + (Yl + Y2) . -\ + w2. 5 1. 5 (c) 91 From (a) and (b), a general solution of the nonhomogeneous system is gjven by (d) The reduced row echelon form of the ..
Contemporary Linear Algebra, Student Solutions Manual by Howard Anton, Robert C. Busby