Hipi Zhdripi i Matematikës/1098

$=\left[\begin{array}{ccc}9& 6& 0\\ 0& 3& -6\\ 18& 12& -3\end{array}\right]+\left[\begin{array}{ccc}-5& 0& 0\\ 0& -5& 0\\ 0& 0& -5\end{array}\right]=\left[\begin{array}{ccc}4& 6& 0\\ 0& -2& -6\\ 18& 12& -8\end{array}\right]$ respektivisht $X=\left[\begin{array}{ccc}9& 3& 0\\ 0& -1& -3\\ 9& 6& -4\end{array}\right]$ 4.1. TRANSPONIMI I MATRICËS        Le të jetë $M$ bashkësia e matricave kurse $A=[a_{ik}{]}_{m,n}$, çfarëdo një matricë e bashkësisë $M$.        P ë r k u f i z i m i  4.1.1. - Veprimi $\tau$ i cili rreshtat e matricës $A$ i trunsforman në shtylla përkatëse e shtyllat në rreshta përkatës quhet transponim i matricës.        Matricë e transponuar e matricës $A=[a_{ik}{]}_{m.n}$ shënohet me $A^{\tau }$ ose $A^{\prime }$, pra: $\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ \cdots & \cdots & \cdots & \cdots \\ \cdots & \cdots & \cdots & \cdots \\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right]\stackrel{p\ddot{e}rk}{=}\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{m1}\\ a_{21}& a_{22}& \cdots & a_{m2}\\ \cdots & \cdots & \cdots & \cdots \\ \cdots & \cdots & \cdots & \cdots \\ a_{1n}& a_{2n}& \cdots & a_{mn}\end{array}\right]$ (...22)        Me transponimin e matricës njështyllore përftohet matrica njërreshtore dhe e anasjellta, pra: ${\left[\begin{array}{c}{a}_{11}\\ a_{21}\\ ⋮\\ a_{n1}\end{array}\right]}^{\prime }=\left[\begin{array}{cccc}{a}_{11},& a_{21},& \dots ,& a_{n1}\end{array}\right];{\left[\begin{array}{cccc}{a}_{11},& a_{12},& \dots ,& a_{1n}\end{array}\right]}^{\prime }=\left[\begin{array}{c}{a}_{11}\\ a_{12}\\ ⋮\\ a_{1n}\end{array}\right]$ (...23) ndërkaq me transponimin e matricës simetrike $A$ përftohet përsëri matrica $A$, d.m.th.: $A^{\prime }=A$.        Për veprimin e transponimit të matricave vlejn këto ligje:         (d1) $(A^{\prime }{)}^{\prime }=A$ ; (d2) $(A+B{)}^{\prime }=A^{\prime }+B^{\prime }$ ; (d3) $(\alpha A{)}^{\prime }=\alpha A^{\prime }$ ; (d4) $(AB{)}^{\prime }=B^{\prime }{A}^{\prime }$ .        Të vërtetojmë p.sh. formulën: $(AB{)}^{\prime }=B^{\prime }{A}^{\prime }$.        Le të supozojmë se matricat $A$, $B$ janë: $A=[a_{ij}{]}_{m,n}B=[b_{jk}{]}_{n,p}$, atëherë matrica $B^{\prime }$ do të jetë e tipit $p\times n$, kurse $A^{\prime }$ e tipit $n\times m$, çka do të thotë se ekziston prodhimi $B^{\prime }{A}^{\prime }$.

< 1097 faqe - 1098 - 1099 > 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100+ 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 200+ 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 300+ 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 400+ 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 500+ 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

< 1097 faqe - 1098 - 1099 >